Solitary waves for linearly coupled nonlinear Schrodinger equations with inhomogeneous coefficients

TL;DR

This paper investigates solitary wave solutions in a system of linearly coupled nonlinear Schrödinger equations with inhomogeneous coefficients, relevant to Bose-Einstein condensates and optical systems, proving existence of specific homoclinic solutions.

Contribution

It introduces a new existence proof for two types of solitary wave solutions in inhomogeneous coupled nonlinear Schrödinger systems using fixed point theory.

Findings

Existence of two types of homoclinic solutions to the origin.

Application of Krasnoselskii fixed point theorem in this context.

Relevance to physical systems like Bose-Einstein condensates and optical fibers.

Abstract

Motivated by the study of matter waves in Bose-Einstein condensates and coupled nonlinear optical systems, we study a system of two coupled nonlinear Schrodinger equations with inhomogeneous parameters, including a linear coupling. For that system we prove the existence of two different kinds of homoclinic solutions to the origin describing solitary waves of physical relevance. We use a Krasnoselskii fixed point theorem together with a suitable compactness criterion.