Wave Operators for the Coupled Klein-Gordon-Schrödinger Equations in Two Space Dimensions

Abstract

In this paper, the scattering theory for the coupled Klein-Gordon-Schrödinger equation with the Yukawa type interaction in two space dimensions is studied. The scattering problem for this equation belongs to the borderline between the short range case and the long range one. The existence of the wave operators to this equation for small scattered states is proved without any restrictions on the support of the Fourier transform of them.