American Institute of Mathematical Sciences

January & February  2004, 10(1&2): 387-396. doi: 10.3934/dcds.2004.10.387

Scattering theory for a particle coupled to a scalar field

 1 Institute of Mathematics, University of Vienna, Boltzmanngasse 9, 1090 Vienna, Austria 2 Department of Mechanics and Mathematics, Moscow State University, Moscow 119899, Russian Federation 3 Zentrum Mathematik, TU München, 80290 München, Germany

Received  February 2002 Revised  April 2003 Published  October 2003

We establish soliton-like asymptotics for finite energy solutions to classical particle coupled to a scalar wave field. Any solution that goes to infinity as $t\to\infty$ converges to a sum of traveling wave and of outgoing free wave. The convergence holds in global energy norm. The proof uses a non-autonomous integral inequality method.
Citation: Valery Imaikin, Alexander Komech, Herbert Spohn. Scattering theory for a particle coupled to a scalar field. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 387-396. doi: 10.3934/dcds.2004.10.387
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