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Long-time asymptotics for a classical particle interacting with a scalar wave field
Authors:Alexander Komechl  Herbert Spohn  Markus Kunze
Institution:1. Department of Mechanics , Moscow, 119899, Russia E-mail: $f:komech@sci.1pi.ac.r$ef:;2. Ludwig-Maximilians-Universitat , Germany E-mail: spohn@stat.physik.uni-muenchen.de;3. Mathematisches Institut der Universitat Koln , Germany E-mail: mkunze@mi.uni-koeln.de
Abstract:We consider the Harniltonian system consisting of scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subject to a confining external potential. The stationary solutions of the system are a Coulomb type wave field centered at those particle positions for which the external force vanishes. We prove that solutions of finite energy converge, in suitable local energy seminorms, to the set of stationary solutions in the long time limit t f oo. The rate of relaxation to a stable stationary solution is determined by spatial decay of initial data. 'Supported partly by French-Russian A.M.Liapunov Center of Moscow State University, by research grants of RFBR (9601-00527) and of Volkswagen-Stiftung.
Keywords:Generalized Korteweg–de Vries equations  Smooth solutions  Solitons
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