{
  "id": "1009.0325",
  "version": "v2",
  "published": "2010-09-02T04:17:54.000Z",
  "updated": "2013-06-03T01:56:30.000Z",
  "title": "Remarks on Scattering Properties of the Solution to a Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities",
  "authors": [
    "Xianfa Song"
  ],
  "comment": "18 pages, withdraw this paper",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the Cauchy problem of Nonlinear Schr\\\"{o}dinger equation \\begin{align*} \\left\\{\\begin{array}{ll}&i u_t+\\Delta u=\\lambda_1|u|^{p_1}u+\\lambda_2|u|^{p_2}u, \\quad t\\in\\mathbb{R}, \\quad x\\in\\mathbb{R}^N &u(0,x)=\\varphi(x), \\quad x\\in\\mathbb{R}^N, \\end{array} \\right. \\end{align*} where $N\\geq 3$, $0<p_1<p_2<\\frac{4}{N-2}$, $\\lambda_1$ and $\\lambda_2$ are real constants. Using the methods in \\cite{Cazenave2} and analyzing the interaction between the nonlinearity $\\lambda_1|u|^{p_1}u$ and $\\lambda_2|u|^{p_2}u$, we not only partly solve the open problems of Terence Tao, Monica Visan and Xiaoyi Zhang's \\cite{Tao} but also obtain other scattering properties of the solutions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-03T01:56:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55"
    ],
    "keywords": [
      "nonlinear schrödinger equation",
      "nonlinearity",
      "scattering properties",
      "power-type nonlinearities",
      "real constants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.0325S"
    }
  }
}