Periodic modulations controlling Kuznetsov–Ma soliton formation in nonlinear Schrödinger equations

Abstract

We analyze the exact Kuznetsov-Ma soliton solution of the one-dimensional nonlinear Schrödinger equation in the presence of periodic modulations satisfying an integrability condition. We show that, in contrast to the case without modulation, the Kuznetsov-Ma soliton develops multiple compression points whose number, shape and position are controlled both by the intensity of the modulation and by its frequency. In addition, when this modulation frequency is a rational multiple of the natural frequency of the Kutzetsov-Ma soliton, a scenario similar to a nonlinear resonance is obtained: in this case the spatial oscillations of the Kuznetsov-Ma soliton's intensity are periodic. When the ratio of the two frequencies is irrational, the soliton's intensity is a quasiperiodic function. A striking and important result of our analysis is the possibility to suppress any component of the output spectrum of the Kuznetsov-Ma soliton by a judicious choice of the amplitude and frequency of the modulation. I.

Modulation instability in dispersion oscillating fibers

“…Finally, we would like to mention that the impact of periodic dispersion has been investigated theoretically on temporal structures associated with the nonlinear regime of MI such as Kuznetsov-Ma breathers. It is shown that it strongly modifies their dynamics [110,111] , but up to know no experimental demonstration have been reported.…”