Scattering theory for a particle coupled to a scalar field

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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

Valery Imaikin ^1, , Alexander Komech ^2, and Herbert Spohn ^3,

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

Abstract
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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.

Keywords: soliton-like asymptotics, solitons, scattering states., scattering solutions, weak interaction, classical particle, particle density, Scalar wave ﬁeld, smooth coupling.

Mathematics Subject Classification: 37K4.

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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