{
  "id": "1706.06252",
  "version": "v1",
  "published": "2017-06-20T03:13:50.000Z",
  "updated": "2017-06-20T03:13:50.000Z",
  "title": "Global Well-posedness and soliton resolution for the Derivative Nonlinear Schrödinger equation",
  "authors": [
    "Robert Jenkins",
    "Jiaqi Liu",
    "Peter Perry",
    "Catherine Sulem"
  ],
  "comment": "91 pages, 7 figures",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the Derivative Nonlinear Schr\\\"odinger equation for general initial conditions in weighted Sobolev spaces that can support bright solitons (but excluding spectral singularities). We prove global well-posedness and give a full description of the long- time behavior of the solutions in the form of a finite sum of localized solitons and a dispersive component. At leading order and in space-time cones, the solution has the form of a multi-soliton whose parameters are slightly modified from their initial values by soliton-soliton and soliton-radiation interactions. Our analysis provides an explicit expression for the correction dispersive term. We use the nonlinear steepest descent method of Deift and Zhou revisited by the $\\bar{\\partial}$-analysis of Dieng-McLaughlin and complemented by the recent work of Borghese-Jenkins-McLaughlin on soliton resolution for the focusing nonlinear Schr\\\"odinger equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-20T03:13:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "37K15",
      "37K40",
      "35A01",
      "35P25"
    ],
    "keywords": [
      "derivative nonlinear schrödinger equation",
      "global well-posedness",
      "soliton resolution",
      "nonlinear steepest descent method",
      "general initial conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 91,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}