{
  "id": "0802.3129",
  "version": "v1",
  "published": "2008-02-21T15:12:28.000Z",
  "updated": "2008-02-21T15:12:28.000Z",
  "title": "An explicit finite difference scheme for the Camassa-Holm equation",
  "authors": [
    "Giuseppe Maria Coclite",
    "Kenneth H. Karlsen",
    "Nils Henrik Risebro"
  ],
  "comment": "45 pages, 6 figures",
  "categories": [
    "math.AP",
    "math.NA"
  ],
  "abstract": "We put forward and analyze an explicit finite difference scheme for the Camassa-Holm shallow water equation that can handle general $H^1$ initial data and thus peakon-antipeakon interactions. Assuming a specified condition restricting the time step in terms of the spatial discretization parameter, we prove that the difference scheme converges strongly in $H^1$ towards a dissipative weak solution of Camassa-Holm equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-02-21T15:12:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35G25",
      "35L05",
      "65M06",
      "65M12"
    ],
    "keywords": [
      "explicit finite difference scheme",
      "camassa-holm equation",
      "camassa-holm shallow water equation",
      "spatial discretization parameter",
      "difference scheme converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.3129C"
    }
  }
}