{
  "id": "1311.0665",
  "version": "v3",
  "published": "2013-11-04T12:10:04.000Z",
  "updated": "2014-03-21T13:53:59.000Z",
  "title": "Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations",
  "authors": [
    "Thomas Duyckaerts",
    "Carlos E. Kenig",
    "Frank Merle"
  ],
  "comment": "New version taking into account suggestions by the referees. To appear in CPAA",
  "categories": [
    "math.AP"
  ],
  "abstract": "Consider a bounded solution of the focusing, energy-critical wave equation that does not scatter to a linear solution. We prove that this solution converges in some weak sense, along a sequence of times and up to scaling and space translation, to a sum of solitary waves. This result is a consequence of a new general compactness/rigidity argument based on profile decomposition. We also give an application of this method to the energy-critical Schr\\\"odinger equation.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-21T13:53:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "35L71",
      "35B40"
    ],
    "keywords": [
      "bounded solution",
      "schrödinger equations",
      "dispersive equations",
      "application",
      "general compactness/rigidity argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.0665D"
    }
  }
}