On Scattering of Solitons for Maxwell Equation Coupled to a Particle

Details On Scattering of Solitons for Maxwell Equation Coupled to a Particle On Scattering of Solitons for Maxwell Equation Coupled to a Particle

2008-07-12

arxiv.org/abs/0807.1972v2

Physics

Mathematical Physics

35 pages

Scientific paper

We establish long time soliton asymptotics for the nonlinear system of Maxwell equations coupled to a charged particle. The coupled system has a six dimensional manifold of soliton solutions. We show that in the long 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 of the free Maxwell equations. It is assumed that the charge density satisfies the Wiener condition. The proof further develops the general strategy based on the 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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