Title Scattering of Solitons for Schrödinger Equation Coupled to a Particle

Alexander Komech, Elena Kopylova

Published 2006-09-22Version 1

We establish soliton-like asymptotics for finite energy solutions to the Schr\"odinger equation coupled to a nonrelativistic classical particle. Any solution with initial state close to the solitary manifold, converges to a sum of traveling wave and outgoing free wave. The convergence holds in global energy norm. The proof uses spectral theory and the symplectic projection onto solitary manifold in the Hilbert phase space.