{
  "id": "0811.4221",
  "version": "v1",
  "published": "2008-11-26T04:36:16.000Z",
  "updated": "2008-11-26T04:36:16.000Z",
  "title": "Wellposedness of Cauchy problem for the Fourth Order Nonlinear Schrödinger Equations in Multi-dimensional Spaces",
  "authors": [
    "Chengchun Hao",
    "Ling Hsiao",
    "Baoxiang Wang"
  ],
  "comment": "28 pages",
  "journal": "J. Math. Anal. Appl., 328(1), 58-83, 2007",
  "doi": "10.1016/j.jmaa.2006.05.031",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the wellposedness of Cauchy problem for the fourth order nonlinear Schr\\\"odinger equations i\\partial_t u=-\\eps\\Delta u+\\Delta^2 u+P((\\partial_x^\\alpha u)_{\\abs{\\alpha}\\ls 2}, (\\partial_x^\\alpha \\bar{u})_{\\abs{\\alpha}\\ls 2}),\\quad t\\in \\Real, x\\in\\Real^n, where $\\eps\\in\\{-1,0,1\\}$, $n\\gs 2$ denotes the spatial dimension and $P(\\cdot)$ is a polynomial excluding constant and linear terms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-26T04:36:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35G25",
      "35A07"
    ],
    "keywords": [
      "fourth order nonlinear schrödinger equations",
      "cauchy problem",
      "multi-dimensional spaces",
      "wellposedness",
      "spatial dimension"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.4221H"
    }
  }
}