{
  "id": "1210.1315",
  "version": "v1",
  "published": "2012-10-04T07:11:03.000Z",
  "updated": "2012-10-04T07:11:03.000Z",
  "title": "Rarefaction pulses for the Nonlinear Schrodinger Equation in the transonic limit",
  "authors": [
    "David Chiron",
    "Mihai Maris"
  ],
  "comment": "48 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate the properties of finite energy travelling waves to the nonlinear Schrodinger equation with nonzero conditions at infinity for a wide class of nonlinearities. In space dimension two and three we prove that travelling waves converge in the transonic limit (up to rescaling) to ground states of the Kadomtsev-Petviashvili equation. Our results generalize an earlier result of F. Bethuel, P. Gravejat and J-C. Saut for the two-dimensional Gross-Pitaevskii equation, and provide a rigorous proof to a conjecture by C. Jones and P. H. Roberts about the existence of an upper branch of travelling waves in dimension three.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-04T07:11:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35C07",
      "35B40",
      "35Q55",
      "35Q53"
    ],
    "keywords": [
      "nonlinear schrodinger equation",
      "transonic limit",
      "rarefaction pulses",
      "two-dimensional gross-pitaevskii equation",
      "finite energy travelling waves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.1315C"
    }
  }
}