{
  "id": "1310.2388",
  "version": "v1",
  "published": "2013-10-09T08:23:48.000Z",
  "updated": "2013-10-09T08:23:48.000Z",
  "title": "On the Gross-Pitaevskii equation with pumping and decay: stationary states and their stability",
  "authors": [
    "Jesús Sierra",
    "Aslan Kasimov",
    "Peter Markowich",
    "Rada-Maria Weishäupl"
  ],
  "comment": "26 pages, 23 figures",
  "categories": [
    "math.NA",
    "math.AP"
  ],
  "abstract": "We investigate the behavior of solutions of the complex Gross-Pitaevskii equation, a model that describes the dynamics of pumped decaying Bose-Einstein condensates. The stationary radially symmetric solutions of the equation are studied and their linear stability with respect to two-dimensional perturbations is analyzed. Using numerical continuation, we calculate not only the ground state of the system, but also a number of excited states. Accurate numerical integration is employed to study the general nonlinear evolution of the system from the unstable stationary solutions to the formation of stable vortex patterns.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-09T08:23:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary states",
      "general nonlinear evolution",
      "stationary radially symmetric solutions",
      "complex gross-pitaevskii equation",
      "vortex patterns"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.2388S"
    }
  }
}