Title Scattering of Solitons for Schrödinger Equation Coupled to a Particle

Details Title Scattering of Solitons for Schrödinger Equation Coupled to a Particle Title Scattering of Solitons for Schrödinger Equation Coupled to a Particle

2006-09-22

arxiv.org/abs/math/0609649v1

Russian J. Math. Phys. 13 (2006), no. 2, 158-187

Mathematics

Analysis of PDEs

32 pages

Scientific paper

10.1134/S106192080602004X

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.

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