Stability analysis of breathers for coupled nonlinear Schrodinger equations

TL;DR

This paper analyzes the spectral and nonlinear stability of breather solutions in coupled nonlinear Schrödinger equations, revealing conditions under which these solutions remain stable.

Contribution

It provides a novel stability analysis of breathers and vector solitons in CNLS equations using spectral methods and Lyapunov techniques, leveraging integrability properties.

Findings

Non-degenerate vector solitons are spectrally stable despite negative Krein signature eigenvalues.

Breathers exhibit nonlinear stability proven via Lyapunov methods and squared eigenfunctions.

Spectral stability persists even with embedded or isolated eigenvalues in the linearized operator.

Abstract

We investigate the spectral stability of non-degenerate vector soliton solutions and the nonlinear stability of breather solutions for the coupled nonlinear Schrodinger (CNLS) equations. The non-degenerate vector solitons are spectrally stable despite the linearized operator admits either embedded or isolated eigenvalues of negative Krein signature. The nonlinear stability of breathers is obtained by the Lyapunov method with the help of the squared eigenfunctions due to integrability of the CNLS equations.