Long range scattering and modified wave operators for the wave-Schrodinger system

We study the theory of scattering for the system consisting of a Schrodinger equation and a wave equation with a Yukawa type coupling in space dimension 3. We prove in particular the existence of modified wave operators for that system with no size restriction on the data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators. The method consists in solving the wave equation, substituting the result into the Schrodinger equation, which then becomes both nonlinear and nonlocal in time, and treating the latter by the method previously used for a family of generalized Hartree equations with long range interactions.