Scattering theory for a particle coupled to a scalar field

Valery Imaikin; Alexander Komech; Herbert Spohn

doi:10.3934/dcds.2004.10.387

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2004, Volume 10, Issue 1&2: 387-396. Doi: 10.3934/dcds.2004.10.387

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Scattering theory for a particle coupled to a scalar field

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

Received: January 31, 2002

Revised: March 31, 2003

Published: December 2003

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Abstract

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.

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Mathematics Subject Classification: 37K40.

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