abstract: 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.
authors.affiliation: Faculty of Mathematics, TU Munich, Garching, 85747, Germany.
authors.forename: Valery
authors.initials: V
authors.lastname: Imaykin
authors.forename: Alexander
authors.initials: A
authors.lastname: Komech
authors.forename: Boris
authors.initials: B
authors.lastname: Vainberg