{
  "id": "1801.08386",
  "version": "v1",
  "published": "2018-01-25T12:54:52.000Z",
  "updated": "2018-01-25T12:54:52.000Z",
  "title": "Conserved energies for the one dimensional Gross-Pitaevskii equation: small energy case",
  "authors": [
    "Herbert Koch",
    "Xian Liao"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We derive in this paper a family of conserved energies for the one dimensional Gross-Pitaevskii equation in the small energy case, which describe all the $H^s$, $s>\\frac 12$ regularities of the solutions. We endow the energy space with a metric to make it a complete metric space and study its topological property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-25T12:54:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dimensional gross-pitaevskii equation",
      "small energy case",
      "conserved energies",
      "complete metric space",
      "energy space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}