Soliton acceleration by dispersive radiation: a contribution to rogue waves?

Abstract: Rogue waves are solitary waves with extreme amplitudes, which appear to be a ubiquitous phenomenon in nonlinear wave propagation, with the requirement for a nonlinearity being their only unifying characteristics. While many mechanisms have been demonstrated to explain the appearance of rogue waves in a specific system, there is no known generic mechanism or general set of criteria shown to rule their appearance. Presupposing only the existence of a nonlinear Schr\"odinger-type equation together with a concave dispersion profile around a zero dispersion wavelength we demonstrate that solitons may experience acceleration and strong reshaping due to the interaction with continuum radiation, giving rise to extreme-value phenomena. The mechanism is independent of the optical Raman effect. A strong increase of the peak power is accompanied by a mild increase of the pulse energy and carrier frequency, whereas the photon number of the soliton remains practically constant. This reshaping mechanism is particularly robust and may explain the appearance of rogue waves in a large class of systems.