Scattering of solitons for coupled wave-particle equations

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• 作者：Valery Imaykin^a ; ¹ ; ^{ivm61@mail.ru} ; Alexander Komech^b ; ¹ ; ² ; ^{alexander.komech@univie.ac.at} ; Boris Vainberg^c ; ³ ; ^{brvainbe@uncc.edu}
• 关键词：Infinite-dimensional Hamiltonian system ; Field-particle interaction ; Solitary manifold ; Soliton-type asymptotics ; Symplectic projection ; Linearization
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 出版时间：15 May 2012
• 年：2012
• 卷：389
• 期：2
• 页码：713-740
• 全文大小：358 K

文摘

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.