{
  "id": "1006.2618",
  "version": "v2",
  "published": "2010-06-14T07:24:20.000Z",
  "updated": "2010-11-22T09:15:38.000Z",
  "title": "Scattering of Solitons for Coupled Wave-Particle Equations",
  "authors": [
    "Valery Imaykin",
    "Alexander Komech",
    "Boris Vainberg"
  ],
  "comment": "31 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-11-22T09:15:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q51",
      "35Q70",
      "37K40"
    ],
    "keywords": [
      "coupled wave-particle equations",
      "charge density satisfies wiener condition",
      "solitary manifold",
      "long time soliton asymptotics",
      "free wave equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.2618I"
    }
  }
}