Breather and Rogue Wave solutions of a Generalized Nonlinear Schrodinger Equation

TL;DR

This paper uses Darboux transformation to generate breather and rogue wave solutions for a generalized nonlinear Schrödinger equation, revealing how higher-order effects influence wave compression in nonlinear fiber and spin chain models.

Contribution

It introduces a method to derive higher-order breather and rogue wave solutions for a generalized NLS equation with higher-order nonlinear effects.

Findings

Higher-order effects cause wave compression.

Solutions applicable to fiber optics and spin chains.

Parameter $ extgamma_1$ controls nonlinear wave behavior.

Abstract

In this paper, using the Darboux transformation, we demonstrate the generation of first order breather and higher-order rogue waves from a generalized nonlinear Schr\"odinger equation with several higher-order nonlinear effects representing femtosecond pulse propagation through nonlinear silica fiber. The same nonlinear evolution equation can also describes the soliton-type nonlinear excitations in classical Heisenberg spin chain. Such solutions have a parameter $\gamma_1$, denoting the strength of the higher-order effects. From the numerical plots of the rational solutions, the compression effects of the breather and rogue waves produced by $\gamma_1$ are discussed in detail.