{
  "id": "1512.04762",
  "version": "v1",
  "published": "2015-12-15T12:46:25.000Z",
  "updated": "2015-12-15T12:46:25.000Z",
  "title": "Asymptotics of step-like solutions for the Camassa-Holm equation",
  "authors": [
    "Alexander Minakov"
  ],
  "comment": "54 p, 40 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the long-time asymptotics of solution of the Cauchy problem for the Camassa-Holm equation with a step-like initial datum. By using the nonlinear steepest descent method and the so-called $g$-function approach, we show that the Camassa-Holm equation exhibits a rich structure of sharply separated regions in the $x,t$-half-plane with qualitatively different asymptotics, which can be described in terms of a sum of modulated finite-gap hyperelliptic or elliptic functions and a finite number of solitons.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-15T12:46:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37K10",
      "37K15",
      "37K40",
      "35B40",
      "37K05"
    ],
    "keywords": [
      "camassa-holm equation",
      "step-like solutions",
      "nonlinear steepest descent method",
      "cauchy problem",
      "long-time asymptotics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151204762M"
    }
  }
}