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Orbital Instability of Standing Waves for the Klein-Gordon-Zakharov System

Abstract This paper deals with the instability of the ground state solitary wave solution to the Klein-Gordon-Zakharov system in three space dimensions with c ≥ 1, which is a model to describe the Langmuir turbulence in plasma. First we construct a suitable constrained variational problem and obtain the existence of the standing waves with ground state by using variational calculus and scaling argument. Then by defining invariant sets and applying some priori estimates, we prove the orbital instability of the ground state in the following sense: in each neighborhood of it, there exists a solution whose energy diverges in finite or infinite time.