Stability of the standing waves for a class of coupled nonlinear Klein-Gordon equations (Q993677)

The paper deals with the stability of standing waves for the system \(u_{tt}-\Delta u+u=(p+1)| u| ^{p-1}| v| ^{q+1}u,\) \(v_{tt}-\Delta v+v=(q+1)| v| ^{q-1}| u| ^{p+1}v,\; t>0,\;x\in \mathbb R^{N},\) where \(N\geq 3\), \(0<p,q<2/(N-2)\) and \(p+q<4/N\). The authors establish the existence of standing waves of the lowest energy in the energy norm, study their behavior as functions of the frequency and give the sufficient conditions under which the standing waves are stable.