In this paper, we study the persistence of spatial analyticity for solutions to Klein-Gordon-Schrödinger system, which describes a physical system nucleon field interacting with neutral meson field, analytic initial data. Unlike case single nonlinear dispersive equation, not much is known about systems as it harder show coupled equations simultaneously. The only results so far are rather recent...

We study here instability problems of standing waves for the nonlinear Klein-Gordon equations and solitary waves for the generalized Boussinesq equations. It is shown that those special wave solutions may be strongly unstable by blowup in finite time, depending on the range of the wave’s frequency or the wave’s speed of propagation and on the nonlinearity.