{
  "id": "1302.3326",
  "version": "v2",
  "published": "2013-02-14T07:32:25.000Z",
  "updated": "2013-11-06T19:33:27.000Z",
  "title": "Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation",
  "authors": [
    "Aleksandr L. Lisok",
    "Aleksandr V. Shapovalov",
    "Andrey Yu. Trifonov"
  ],
  "journal": "SIGMA 9 (2013), 066, 21 pages",
  "doi": "10.3842/SIGMA.2013.066",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the symmetry properties of an integro-differential multidimensional Gross-Pitaevskii equation with a nonlocal nonlinear (cubic) term in the context of symmetry analysis using the formalism of semiclassical asymptotics. This yields a semiclassically reduced nonlocal Gross-Pitaevskii equation, which can be treated as a nearly linear equation, to determine the principal term of the semiclassical asymptotic solution. Our main result is an approach which allows one to construct a class of symmetry operators for the reduced Gross-Pitaevskii equation. These symmetry operators are determined by linear relations including intertwining operators and additional algebraic conditions. The basic ideas are illustrated with a 1D reduced Gross-Pitaevskii equation. The symmetry operators are found explicitly, and the corresponding families of exact solutions are obtained.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-06T19:33:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "intertwining operators",
      "symmetry operators",
      "integro-differential multidimensional gross-pitaevskii equation",
      "additional algebraic conditions",
      "semiclassically reduced nonlocal gross-pitaevskii equation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2013,
      "month": "Nov",
      "volume": 9,
      "pages": "066"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013SIGMA...9..066L"
    }
  }
}