  In this paper we study small amplitude solutions of nonlinear Klein Gordon
equations with a potential. Under smoothness and decay assumptions on the
potential and a genericity assumption on the nonlinearity, we prove that all
small amplitude initial data with finite energy give rise to solutions
asymptotically free. In the case where the linear system has at most one bound
state the result was already proved by Soffer and Weinstein: we obtain here a
result valid in the case of an arbitrary number of possibly degenerate bound
states. The proof is based on a combination of Birkhoff normal form techniques
and dispersive estimates.
