Scattering theory for a particle coupled to a scalar field
Valery Imaikin - Institute of Mathematics, University of Vienna, Boltzmanngasse 9, 1090 Vienna, Austria (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.
Received: February 2002; Revised: April 2003; Published: October 2003.
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