On traveling waves and global existence for a nonlinear Schr\"odinger system with three waves interaction

TL;DR

This paper investigates the existence of traveling wave solutions and global existence for a three-component nonlinear Schrödinger system related to plasma Raman amplification, highlighting the impact of the absence of Galilean symmetry.

Contribution

It introduces new existence results for traveling waves and global solutions in a nonlinear Schrödinger system lacking Galilean symmetry, using variational methods.

Findings

Existence of traveling wave solutions under non-mass resonance conditions

Global existence results for oscillating initial data

Absence of Galilean symmetry influences the system's behavior

Abstract

In this paper, we consider three components system of nonlinear Schr\"odinger equations related to the Raman amplification in a plasma. By using variational method, a new result on the existence of traveling wave solutions are obtained under the non-mass resonance condition. We also study the new global existence result for oscillating data. Both of our results essentially due to the absence of Galilean symmetry in the system.