Soliton - Like Asymptotics for a Classical ParticleInteracting with a Scalar Wave Field

Interacting with a Scalar Wave Field Alexander Komech1 Department of Mechanics and Mathematics of Moscow State University, Moscow 119899, Russia email: [email protected] Herbert Spohn Theoretische Physik, Ludwig-Maximilians-Universit at Theresienstrasse 37, D-80333 M unchen, Germany email: [email protected] AbstractWe consider a scalar wave eld translation invariantly coupled to a single particle. This Hamiltonian system admits soliton-like solutions, where the particle and comoving eld travel with constant velocity. We prove that a solution of nite energy converges, in suitable local energy seminorms, to some soliton-like solutions in the long time limit t! 1.