On the linear stability of simple and semi‐simple periodic waves for a system of cubic Klein–Gordon equations

Abstract

AbstractWe study the linear stability of traveling wave solutions for the nonlinear wave equation and coupled nonlinear wave equations. It is shown that periodic waves of the dnoidal type are spectrally unstable with respect to co‐periodic perturbations. Our arguments rely on a careful spectral analysis of various self‐adjoint operators, both scalar and matrix and on instability index count theory for Hamiltonian systems.