Orbital Instability of Standing Waves for the Coupled Nonlinear Klein-Gordon Equations (Journal of Partial Differential Equations, 2020)
This paper deals with a type of standing waves for the coupled nonlinear Klein-Gordon equations in three space dimensions. First we construct a suitable constrained variational problem and obtain the existence of the standing waves with ground state by using variational argument. Then we prove the orbital instability of the standing waves by defining invariant sets and applying some priori estimates.
Keywords: Orbital instability; standing wave; coupled Klein-Gordon equations; invariant set