Soliton type asymptotics for the Klein-Gordon equation coupled to nonlinear oscillator

Abstract The long-time asymptotics are obtained for finite energy solutions of the 1D Klein-Gordon equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U (1). For initial states close to a solitary wave, the solution converges to a sum of another solitary wave and dispersive wave which is a solution to the free Klein-Gordon equation.