{
  "id": "math/0510080",
  "version": "v1",
  "published": "2005-10-04T17:38:53.000Z",
  "updated": "2005-10-04T17:38:53.000Z",
  "title": "Scattering for the Gross-Pitaevskii equation",
  "authors": [
    "S. Gustafson",
    "K. Nakanishi",
    "T. -P. Tsai"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We investigate the asymptotic behavior at time infinity of solutions close to a non-zero constant equilibrium for the Gross-Pitaevskii (or Ginzburg-Landau Schroedinger) equation. We prove that, in dimensions larger than 3, small perturbations can be approximated at time infinity by the linearized evolution, and the wave operators are homeomorphic around 0 in certain Sobolev spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-10-04T17:38:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "82D50"
    ],
    "keywords": [
      "gross-pitaevskii equation",
      "time infinity",
      "non-zero constant equilibrium",
      "solutions close",
      "asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10080G"
    }
  }
}