Orbital stability of solitary waves for the Schr odinger-Boussinesq system

TL;DR

This paper proves the orbital stability of solitary waves in a Schrödinger-Boussinesq system using spectral analysis, extending previous results in the field.

Contribution

It introduces a new stability analysis for solitary waves in the Schrödinger-Boussinesq system, expanding upon earlier work with a detailed spectral approach.

Findings

Orbital stability of solitary waves established.

Spectral analysis confirms stability conditions.

Extends previous stability results to a broader system.

Abstract

This paper studies the orbital stability of solitary waves for the following Schr\"{o}dinger-Boussinesq system \begin{equation*} \begin{cases} { \begin{array}{ll} i\varepsilon_t+\varepsilon_{xx}=n\varepsilon+\gamma |\varepsilon|^2\varepsilon, \\ n_{tt}-n_{xx}+ \alpha n_{xxxx}-\beta(n^2)_{xx}=|\varepsilon|^2_{xx}, \end{array} } (t,x)\in \mathbb{R}^2. \end{cases} \end{equation*} By applying the abstract results and detailed spectral analysis, we obtain the orbital stability of solitary waves. The result can be regarded as an extension of the results of \cite{ F-P,H,W}.