{
  "id": "0711.2694",
  "version": "v1",
  "published": "2007-11-16T22:39:35.000Z",
  "updated": "2007-11-16T22:39:35.000Z",
  "title": "Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential",
  "authors": [
    "Dmitry Pelinovsky",
    "Guido Schneider"
  ],
  "comment": "9 pages, 2 figures",
  "categories": [
    "math-ph",
    "math.DS",
    "math.MP"
  ],
  "abstract": "We justify the validity of the discrete nonlinear Schrodinger equation for the tight-binding approximation in the context of the Gross-Pitaevskii equation with a periodic potential. Our construction of the periodic potential and the associated Wannier functions is based on the previous work, while our analysis involving energy estimates and Gronwall's inequality addresses time-dependent localized solutions on large but finite time intervals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-16T22:39:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic potential",
      "gross-pitaevskii equation",
      "tight-binding approximation",
      "inequality addresses time-dependent localized solutions",
      "discrete nonlinear schrodinger equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.2694P"
    }
  }
}