{
  "id": "0809.2035",
  "version": "v5",
  "published": "2008-09-11T16:05:47.000Z",
  "updated": "2010-10-26T20:25:57.000Z",
  "title": "Instability of Standing Waves to the Inhomogeneous Nonlinear Schrödinger Equation with Harmonic Potential",
  "authors": [
    "Jianqing Chen",
    "Yue Liu"
  ],
  "comment": "This paper has been withdrawn by the authors. the paper is already published",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the instability of standing-wave solutions $e^{i\\omega t}\\phi_{\\omega}(x)$ to the inhomogeneous nonlinear Schr\\\"{o}dinger equation $$i\\phi_t=-\\triangle\\phi+|x|^2\\phi-|x|^b|\\phi|^{p-1}\\phi, \\qquad \\in\\mathbb{R}^N, $$ where $ b > 0 $ and $ \\phi_{\\omega} $ is a ground-state solution. The results of the instability of standing-wave solutions reveal a balance between the frequency $\\omega $ of wave and the power of nonlinearity $p $ for any fixed $ b > 0. $",
  "revisions": [
    {
      "version": "v5",
      "updated": "2010-10-26T20:25:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35B35",
      "35A15",
      "35J20"
    ],
    "keywords": [
      "inhomogeneous nonlinear schrödinger equation",
      "harmonic potential",
      "standing waves",
      "instability",
      "standing-wave solutions reveal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.2035C"
    }
  }
}