Sobolev Stability of Plane Wave Solutions to the Nonlinear Schrodinger Equation

TL;DR

This paper investigates the long-term orbital stability of plane wave solutions to the defocusing nonlinear Schrödinger equation within high order Sobolev norms, contributing to the understanding of their stability properties.

Contribution

It provides new results on the Sobolev stability of plane wave solutions to the defocusing NLSE, extending previous stability analyses to higher Sobolev norms.

Findings

Establishes long-time orbital stability in high Sobolev norms

Demonstrates stability of plane waves in the defocusing case

Advances understanding of nonlinear wave stability in Sobolev spaces

Abstract

This article explores the questions of long time orbital stability in high order Sobolev norms of plane wave solutions to the NLSE in the defocusing case.