Riemann problem for the light pulses in optical fibers for the generalized Chen-Lee-Liu equation

Abstract

We provide the classification of possible wave structures evolving from initially discontinuous profiles for the photon fluid propagating in a normal dispersion fiber. The dynamics of light field is described by the generalized Chen-Lee-Liu equation which belong to a family of the nonlinear Schrödinger equations with self-steepening type term appearing due to retardation of the fiber material response to variations of the electromagnetic signal. This equation is also used in investigations of dynamics of modulated wave propagating through a single nonlinear transmission network. We describe its periodic solutions and the corresponding Whitham modulation equations. The wave patterns generated by the initial parameters profiles are composed of different building blocks which are presented in detail. It is shown that evolution dynamics in this case is much richer than that for the nonlinear Schrödinger equation. Complete classification of possible wave structures is given for all possible jump conditions at the discontinuity. Our analytic results are confirmed by numerical simulations.