{
  "id": "math/0405411",
  "version": "v1",
  "published": "2004-05-21T13:12:35.000Z",
  "updated": "2004-05-21T13:12:35.000Z",
  "title": "Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential",
  "authors": [
    "Remi Carles"
  ],
  "comment": "20 pages; survey of previous results",
  "journal": "Commun. Contemp. Math., Vol. 7, No. 4 (2005) 483-508",
  "doi": "10.1142/S0219199705001829",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We review some recent results on nonlinear Schrodinger equations with potential, with emphasis on the case where the potential is a second order polynomial, for which the interaction between the linear dynamics caused by the potential, and the nonlinear effects, can be described quite precisely. This includes semi-classical regimes, as well as finite time blow-up and scattering issues. We present the tools used for these problems, as well as their limitations, and outline the arguments of the proofs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-21T13:12:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35A05",
      "35B30",
      "35B35"
    ],
    "keywords": [
      "nonlinear schrodinger equations",
      "nonlinear effects",
      "second order polynomial",
      "finite time blow-up",
      "linear dynamics"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5411C"
    }
  }
}