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arXiv · 1006.2618

Scattering of Solitons for Coupled Wave-Particle Equations

Valery Imaykin·Alexander Komech·Boris Vainberg
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Abstract

We establish a long time soliton asymptotics for a nonlinear system of wave equation coupled to a charged particle. The coupled system has a six dimensional manifold of soliton solutions. We show that in the large time approximation, any solution, with an initial state close to the solitary manifold, is a sum of a soliton and a dispersive wave which is a solution to the free wave equation. It is assumed that the charge density satisfies Wiener condition which is a version of Fermi Golden Rule, and that the momenta of the charge distribution vanish up to the fourth order. The proof is based on a development of the general strategy introduced by Buslaev and Perelman: symplectic projection in Hilbert space onto the solitary manifold, modulation equations for the parameters of the projection, and decay of the transversal component.

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Valery Imaykin, Alexander Komech, Boris Vainberg. 2010-11-22. Scattering of Solitons for Coupled Wave-Particle Equations. https://arxiv.org/abs/1006.2618

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