Spectral stability of multiple periodic waves for the Schrodinger system with cubic nonlinearity

TL;DR

This paper investigates the existence and spectral stability of multiple periodic wave solutions in a nonlinear Schrödinger system with cubic nonlinearity, using Floquet theory and spectral analysis techniques.

Contribution

It provides new spectral stability and instability results for dnoidal and cnoidal wave solutions in the Schrödinger system, employing Krein signature and Floquet theory.

Findings

Spectral stability results for multiple periodic waves.

Spectral instability conditions identified.

Application of Floquet theory and Krein signature methods.

Abstract

Results concerning the existence and spectral stability and instability of multiple periodic wave solutions for the nonlinear Schr\"odinger system with \textit{dnoidal} and \textit{cnoidal} profile will be determined in this manuscript. The spectral analysis for the corresponding linearized operator is established by using the comparison theorem and tools of Floquet theory. The main results are determined by applying the spectral stability theory in \cite{KapitulaKevrekidisSandstedeI} and \cite{KapitulaKevrekidisSandstedeII} via Krein signature.