Spectral stability for subsonic traveling pulses of the Boussinesq `abc' system

TL;DR

This paper rigorously analyzes the spectral stability of explicit sech^2-like traveling wave solutions of the Boussinesq `abc' system, focusing on cases where parameters satisfy specific inequalities.

Contribution

It provides a complete characterization of spectral stability for explicit solutions of the Boussinesq `abc' system under certain parameter conditions.

Findings

Spectral stability is established for the explicit sech^2-like solutions when a=c<0 and b>0.

The analysis covers all relevant cases for the specified parameter conditions.

The results contribute to understanding the stability properties of traveling waves in the Boussinesq `abc' system.

Abstract

We consider the spectral stability of certain traveling wave solutions of the Boussinesq `abc' system. More precisely, we consider the explicit $sech^2(x)$ like solutions of the form $(\vp(x-w t), \psi(x- w t)=(\vp, const. \vp)$, exhibited by M. Chen (1998) and we provide a complete rigorous characterization of the spectral stability in all cases for which $a=c<0, b>0$.