Self-Localized Solutions of the Kundu-Eckhaus Equation in Nonlinear Waveguides

TL;DR

This study numerically investigates self-localized solutions of the Kundu-Eckhaus equation in nonlinear waveguides, comparing them with nonlinear Schrödinger equation solutions, and explores the existence of solitons under various potentials and nonlinearities.

Contribution

It provides the first numerical analysis of Kundu-Eckhaus equation solitons in waveguides, highlighting conditions for their existence and stability compared to NLSE solutions.

Findings

Single, dual, and N-soliton solutions exist for zero optical potential.

Solitons do not exist in photorefractive lattices with certain optical potentials.

Self-stable solutions with saturable nonlinearity are found for some parameters.

Abstract

In this paper we numerically analyze the 1D self-localized solutions of the Kundu-Eckhaus equation (KEE) in nonlinear waveguides using the spectral renormalization method (SRM) and compare our findings with those solutions of the nonlinear Schrodinger equation (NLSE). We show that single, dual and N-soliton solutions exist for the case with zero optical potentials, i.e. V=0. We also show that these soliton solutions do not exist, at least for a range of parameters, for the photorefractive lattices with optical potentials in the form of V=Io cos^2(x) for cubic nonlinearity. However, self-stable solutions of the KEE with saturable nonlinearity do exist for some range of parameters. We compare our findings for the KEE with those of the NLSE and discuss our results.