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.
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Gaston Tiofack, Saliya Coulibaly, Majid Taki, Stephan de Bièvre, Guillaume Dujardin. Periodic modulations controlling Kuznetsov-Ma soliton formation in nonlinear Schrödinger equations. Physics Letters A, Elsevier, 2017. ⟨hal-01403028⟩

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