Strong instability of standing waves for the nonlinear Klein-Gordon equation and the Klein-Gordon-Zakharov system

摘要

The orbital instability of ground state standing waves e(i omega t)phi(omega)(x) for the nonlinear Klein-Gordon equation has been known in the domain of all frequencies w for the supercritical case and for frequencies strictly less than a critical frequency w(c) in the subcritical case. We prove the strong instability of ground state standing waves for the entire domain above. For the case when the frequency is equal to the critical frequency w(c) we prove strong instability for all radially symmetric standing waves e(i omega ct)phi(x). We prove similar strong instability results for the Klein-Gordon-Zakharov system.