Instability of Standing Waves for Hamiltonian Wave Equations

This paper deals with the standing wave for a Hamiltonian nonlinear wave equation which can be viewed as a representative of the class of equations of interest.On the one hand,by proving a compactness lemma and solving a variational problem,the existence of the standing wave with ground state for the aforementioned equation is proved.On the other hand,the authors derive the instability of the standing wave by applying the potential well argument,the concavity method and an invariant region under the solutio...