{
  "id": "math/0106194",
  "version": "v1",
  "published": "2001-06-22T19:37:19.000Z",
  "updated": "2001-06-22T19:37:19.000Z",
  "title": "Persistent Homoclinic Orbits for Nonlinear Schroedinger Equation Under Singular Perturbation",
  "authors": [
    "Yanguang Charles Li"
  ],
  "comment": "43 pages",
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "Existence of homoclinic orbits in the cubic nonlinear Schr\\\"odinger equation under singular perturbations is proved. Emphasis is placed upon the regularity of the semigroup $e^{\\e t \\pa_x^2}$ at $\\e = 0$. This article is a substantial generalization of \\cite{LMSW96}, and motivated by the effort of Dr. Zeng \\cite{Zen00a} \\cite{Zen00b}. The mistake of Zeng in \\cite{Zen00b} is corrected with a normal form transform approach. Both one and two unstable modes cases are investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-06-22T19:37:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear schroedinger equation",
      "persistent homoclinic orbits",
      "singular perturbation",
      "normal form transform approach",
      "substantial generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......6194L"
    }
  }
}