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Scattering asymptotics for a charged particle coupled to the Maxwell field. (English) Zbl 1316.78002

Summary: 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.{
©2011 American Institute of Physics}

MSC:

78A35 Motion of charged particles
78A60 Lasers, masers, optical bistability, nonlinear optics
35C08 Soliton solutions
78A40 Waves and radiation in optics and electromagnetic theory
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
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