Solitary waves in coupled nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities

TL;DR

This paper develops a Lie group-based method to find explicit solitary wave solutions in coupled nonlinear Schrödinger systems with spatially varying nonlinearities, analyzing their stability and dynamics.

Contribution

It introduces a general Lie group approach to construct explicit solutions for inhomogeneous coupled nonlinear Schrödinger equations, advancing solution techniques and stability analysis.

Findings

Constructed explicit solitary wave solutions

Analyzed linear stability of solutions

Studied dynamical stability of solutions

Abstract

Using Lie group theory we construct explicit solitary wave solutions of coupled nonlinear Schrodinger systems with spatially inhomogeneous nonlinearities. We present the general theory, use it to construct different families of explicit solutions and study their linear and dynamical stability.