Orbital stability of standing waves for a system of nonlinear Schr\"{o}dinger equations with three wave interaction

TL;DR

This paper investigates the existence and orbital stability of standing wave solutions in a three-coupled nonlinear Schrödinger system modeling Raman amplification in plasma, using variational methods and concentration-compactness techniques.

Contribution

It provides a new characterization of standing waves as energy minimizers under multiple mass constraints, establishing their existence and stability.

Findings

Existence of standing wave solutions via variational methods

Orbital stability of these solutions

Characterization of solutions as energy minimizers

Abstract

We study the existence and stability of standing waves solutions of a three-coupled nonlinear Schr\"{o}dinger system related to the Raman amplification in a plasma. By means of the concentration-compacteness method, we provide a characterization of the standing waves solutions as minimizers of an energy functional subject to three independent $L^{2}$ mass constraints. As a consequence, we establish existence and orbital stability of solitary waves.