{
  "id": "0807.1972",
  "version": "v2",
  "published": "2008-07-12T12:26:39.000Z",
  "updated": "2010-12-02T16:42:06.000Z",
  "title": "On Scattering of Solitons for Maxwell Equation Coupled to a Particle",
  "authors": [
    "Valery Imaykin",
    "Alexander Komech",
    "Herbert Spohn"
  ],
  "comment": "35 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-02T16:42:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37K40",
      "35Q51"
    ],
    "keywords": [
      "maxwell equation",
      "establish long time soliton asymptotics",
      "solitary manifold",
      "long time approximation",
      "charge density satisfies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.1972I"
    }
  }
}