Breaking of a wave perturbation via singularity formation for photon fluid in fibers with quintic nonlinearity

Abstract

We consider the wave breaking problem that a simple wave structure with a parabolic or cubic initial function contour propagates to the photon fluid with constant velocity and density of the Gerdjikov-Ivanov equation, and the breaking arises by forming a singularity accompanied the occurrence of a dispersive shock wave (DSW). The description of DSW is obtained by applying the Whitham modulation theory. The correspondence between physical variables and Riemann invariants is two-valued, therefore, we derive the structure of Riemann invariants and two corresponding DSWs under a parabolic or cubic initial profile, and the numerical simulation results are consistent with the theoretical solutions. Meanwhile, the laws of motion of DSWs at the small-amplitude and soliton edge are analyzed respectively.