Nonlinear evolution of modulational instability under the interaction of Kerr nonlinearity with pure higher, even-order dispersion

Abstract

We investigate the nonlinear evolutions of modulation instability (MI) under the interaction of Kerr nonlinearity with pure higher, even-order dispersion (HEOD) by using the truncating method of three-wave mixing. For any HEOD, we find the phase-plane topological structure of the MI changes in three frequency regions whose ranges depend on the order of HEOD. And we present the novel types of nonlinear evolutions of the MI, which do not exist in the case of quadratic dispersion. Taking the pure-sextic dispersion as an example, the theoretical predictions of the MI evolutions are confirmed by numerically solving the modified nonlinear Schrödinger equation. Our results not only further deepen the understanding of MI, but also provide a universal guideline for experimental investigation of nonlinear waves, such as breather solitons or rogue waves excitation, in nonlinear Kerr media with pure HEOD.