{
  "id": "math/0606254",
  "version": "v4",
  "published": "2006-06-11T13:59:13.000Z",
  "updated": "2009-06-13T19:23:03.000Z",
  "title": "A pseudoconformal compactification of the nonlinear Schrödinger equation and applications",
  "authors": [
    "Terence Tao"
  ],
  "comment": "17 pages, no figures, to appear, New York J. Math. This is the final version",
  "categories": [
    "math.AP"
  ],
  "abstract": "We interpret the lens transformation (a variant of the pseudoconformal transformation) as a pseudoconformal compactification of spacetime, which converts the nonlinear Schr\\\"odinger equation (NLS) without potential with a nonlinear Schr\\\"odinger equation with attractive harmonic potential. We then discuss how several existing results about NLS can be placed in this compactified setting, thus offering a new perspective to view this theory.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-06-13T19:23:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55"
    ],
    "keywords": [
      "nonlinear schrödinger equation",
      "pseudoconformal compactification",
      "applications",
      "lens transformation",
      "pseudoconformal transformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6254T"
    }
  }
}