Schr\"odinger system with quintic nonlinearity: spectral stability of multiple sign-changing periodic waves

TL;DR

This paper analyzes the spectral stability of multiple sign-changing periodic standing waves in a nonlinear Schr"odinger system with quintic nonlinearity, using Floquet theory and Krein signature methods.

Contribution

It provides a comprehensive spectral analysis of cnoidal and snoidal solutions, establishing stability criteria for periodic waves with sign changes.

Findings

Spectral stability of certain periodic waves is established.

Instability regions are identified via Krein signature analysis.

The analysis covers both stability and instability conditions.

Abstract

This manuscript investigates the existence and spectral stability of multiple periodic standing wave solutions for a nonlinear Schr\"odinger system. By considering both cnoidal and snoidal profiles, we provide a comprehensive spectral analysis of the associated linearized operators, employing the Floquet theory and comparison theorems. Stability results are derived under periodic perturbations with the same period as the underlying standing waves. Furthermore, we apply the spectral stability theory via Krein signature to determine the spectral stability and instability results.