Propagation of periodic and solitary waves in a highly dispersive cubic-quintic medium with self-frequency shift and self-steepening nonlinearity

TL;DR

This paper investigates the complex behavior of femtosecond light pulses in a highly dispersive cubic-quintic medium, deriving various wave solutions and analyzing their stability considering higher-order effects and nonlinearities.

Contribution

It introduces new analytical solutions for periodic and solitary waves in a generalized higher-order nonlinear Schrödinger equation with self-frequency shift and self-steepening effects.

Findings

Wave profiles depend on dispersion and nonlinearity parameters.

Stable wave solutions are confirmed through numerical simulations.

Existence conditions for wave structures are established.

Abstract

We study the dynamics of femtosecond light pulse propagation in a cubic-quintic medium exhibiting dispersive effect up to the fourth order as well as self-frequency shift and self-steepening nonlinearity. A rich variety of periodic and solitary wave solutions are derived for the governing generalized higher-order nonlinear Schr\"{o}dinger equation in the presence of self-frequency shift and self-steepening effects. It is found that the frequency shift, inverse velocity, amplitude and wave number of both periodic and solitary waves depend on dispersion coefficients and nonlinearity parameters as well. The conditions on optical fiber parameters for the existence of these structures are presented. The stability of these periodic and solitary wave solutions is studied numerically by adding white noise. It is proved by using the numerical split-step Fourier method that the profile of these nonlinear waves remains unchanged during evolution.