{
  "id": "math/0210481",
  "version": "v3",
  "published": "2002-10-31T15:39:46.000Z",
  "updated": "2003-03-14T11:08:11.000Z",
  "title": "Nonlinear Schrodinger equations with repulsive harmonic potential and applications",
  "authors": [
    "Remi Carles"
  ],
  "comment": "Final version, to appear in SIAM J. Math. Anal",
  "journal": "SIAM J. Math. Anal., 35, #4 (2003), 823-843.",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the Cauchy problem for Schrodinger equations with repulsive quadratic potential and power-like nonlinearity. The local problem is well-posed in the same space as that used when a confining harmonic potential is involved. For a defocusing nonlinearity, it is globally well-posed, and a scattering theory is available, with no long range effect for any superlinear nonlinearity. When the nonlinearity is focusing, we prove that choosing the harmonic potential sufficiently strong prevents blow-up in finite time. Thanks to quadratic potentials, we provide a method to anticipate, delay, or prevent wave collapse; this mechanism is explicit for critical nonlinearity.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-03-14T11:08:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35B05",
      "35B40",
      "35P25"
    ],
    "keywords": [
      "nonlinear schrodinger equations",
      "repulsive harmonic potential",
      "nonlinearity",
      "harmonic potential sufficiently strong prevents",
      "applications"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10481C"
    }
  }
}