Linear stability analysis for periodic traveling waves of the Boussinesq equation and the KGZ system

Abstract

The question for linear stability of spatially periodic waves for the Boussinesq equation (the cases $p=2,3$) and the Klein-Gordon-Zakharov system is considered. For a wide class of solutions, we completely and explicitly characterize their linear stability (instability respectively), when the perturbations are taken with the same period $T$. In particular, our results allow us to completely recover the linear stability results, in the limit $T\to \infty$, for the whole line case.

References in corpus (3)

• Local solutions in Sobolev spaces with negative indices for the "good" Boussinesq equation
• Linear stability analysis for traveling waves of second order in time PDE's
• Transverse instability for periodic waves of KP-I and Schrödinger equations

Cited by in corpus (4)

• Linear stability analysis for traveling waves of second order in time PDE's
• The Klein-Gordon-Zakharov equations with the positive fractional power terms and their exact solutions
• An Instability Index Theory for Quadratic Pencils and Applications
• Graphical Krein Signature Theory and Evans-Krein Functions