Linear Stability Analysis for Standing Waves of Second Order in Time Pde’s

We develop a general theory to treat the linear stability of standing waves of second order in time evolutionary PDEs. We apply these results to several concrete examples: the KleinGordon equation, for which we consider both ground states and certain excited states, the KleinGordon-Zakharov system and the beam equation. We also discuss possible applications to some non-standard ground and excited states for the Klein-Gordon model as well as multidimensional traveling waves (not necessarily homoclinic to zero) for general second order equations of this type. In all cases, our abstract results provide a complete characterization of the linear stability of such solutions.