{
  "id": "0902.3804",
  "version": "v1",
  "published": "2009-02-22T16:55:47.000Z",
  "updated": "2009-02-22T16:55:47.000Z",
  "title": "Existence and properties of travelling waves for the Gross-Pitaevskii equation",
  "authors": [
    "Fabrice Béthuel",
    "Philippe Gravejat",
    "Jean-Claude Saut"
  ],
  "journal": "Stationary and time dependent Gross-Pitaevskii equations, A. Farina and J.-C. Saut (Ed.) (2008) 55-104",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper presents recent results concerning the existence and qualitative properties of travelling wave solutions to the Gross-Pitaevskii equation posed on the whole space R^N. Unlike the defocusing nonlinear Schr\\\"odinger equations with null condition at infinity, the presence of non-zero conditions at infinity yields a rather rich and delicate dynamics. We focus on the case N = 2 and N = 3, and also briefly review some classical results on the one-dimensional case. The works we survey provide rigorous justifications to the impressive series of results which Jones, Putterman and Roberts established by formal and numerical arguments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-22T16:55:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q40",
      "35Q53",
      "35Q55",
      "35A05",
      "35B40"
    ],
    "keywords": [
      "gross-pitaevskii equation",
      "properties",
      "one-dimensional case",
      "travelling wave solutions",
      "infinity yields"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.3804B"
    }
  }
}