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

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

2012-02-09

arxiv.org/abs/1202.2133v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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