Stabilization for the Klein-Gordon-Zakharov system

This paper deals with global stability dynamics for the Klein-Gordon-Zakharov system in R-2. We first establish that this system admits a family of linear mode unstable explicit quasi-periodic wave solutions. Next, we prove that the Kelvin-Voigt damping can help to stabilize those linear mode unstable explicit quasi-periodic wave solutions for the Klein-Gordon-Zakharov system in the Sobolev space Hs+1(R-2) x Hs+1(R-2) x Hs+1(R-2) for any s >= 1. Moreover, the Kelvin-Voigt damped Klein-Gordon-Zakharov system admits a unique Sobolev regular solution exponentially convergent to some special solutions (including quasi-periodic wave solutions) of it. Our result can be extended to the n-dimension dissipative Klein-Gordon-Zakharov system for any n >= 1.