  We establish a long time soliton asymptotics for a nonlinear system of wave
equation coupled to a charged particle. The coupled system has a six
dimensional manifold of soliton solutions. We show that in the large time
approximation, any solution, with an initial state close to the solitary
manifold, is a sum of a soliton and a dispersive wave which is a solution to
the free wave equation. It is assumed that the charge density satisfies Wiener
condition which is a version of Fermi Golden Rule, and that the momenta of the
charge distribution vanish up to the fourth order. The proof is based on a
development of the general strategy introduced by Buslaev and Perelman:
symplectic projection in Hilbert space onto the solitary manifold, modulation
equations for the parameters of the projection, and decay of the transversal
component.
