Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Scattering theory for a particle coupled to a scalar field

Pages: 387 - 396, Volume 10, Issue 1/2, January/February 2004      doi:10.3934/dcds.2004.10.387

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Valery Imaikin - Institute of Mathematics, University of Vienna, Boltzmanngasse 9, 1090 Vienna, Austria (email)
Alexander Komech - Department of Mechanics and Mathematics, Moscow State University, Moscow 119899, Russian Federation (email)
Herbert Spohn - Zentrum Mathematik, TU München, 80290 München, Germany (email)

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.

Keywords:  Scalar wave field, classical particle, particle density, smooth coupling,weak interaction, solitons, soliton-like asymptotics, scattering solutions, scattering states.
Mathematics Subject Classification:  37K40.

Received: February 2002;      Revised: April 2003;      Available Online: October 2003.