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Well-posed Cauchy problem and the Hamiltonian form of (2+1) nonlinear equations integrable by inverse scattering transform (2412.16801v1)
Published 21 Dec 2024 in nlin.SI, math-ph, math.FA, and math.MP
Abstract: The Hamiltonian form of the (2+1) nonlinear integrable Schr\"odinger equation and the system of two (2+1) nonlinear analogue of the mKdV equation is proved. A well--posed Cauchy problem is formulated and the solvability of such a problem for the (2+1) nonlinear analogue of the mKdV equation is proved.
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