On the soliton dynamics under slowly varying medium for Nonlinear Schr\"odinger equations

TL;DR

This paper studies how solitons propagate in media that change slowly over space for a generalized nonlinear Schrödinger equation, proving existence, uniqueness, and describing their long-term behavior.

Contribution

It introduces new soliton-like solutions for variable-coefficient nonlinear Schrödinger equations in slowly varying media, with proofs of existence, uniqueness, and detailed behavior analysis.

Findings

Existence of new soliton-like solutions in slowly varying media

Uniqueness of these solutions under broad conditions

Long-term behavior description of the solutions

Abstract

We consider the problem of the soliton propagation, in a slowly varying medium, for a generalized, variable-coefficients nonlinear Schr\"odinger equation. We prove existence and uniqueness of new soliton-like solutions for a large class of slowly varying media. Moreover, we describe for all time the behavior of this new generalized soliton solution.