{
  "id": "1301.1048",
  "version": "v1",
  "published": "2013-01-06T20:09:54.000Z",
  "updated": "2013-01-06T20:09:54.000Z",
  "title": "Focusing Singularity in a Derivative Nonlinear Schrödinger Equation",
  "authors": [
    "Xiao Liu",
    "Gideon Simpson",
    "Catherine Sulem"
  ],
  "comment": "24 pages, 17 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We present a numerical study of a derivative nonlinear Schr\\\"odinger equation with a general power nonlinearity, $|\\psi|^{2\\sigma}\\psi_x$. In the $L^2$-supercritical regime, $\\sigma>1$, our simulations indicate that there is a finite time singularity. We obtain a precise description of the local structure of the solution in terms of blowup rate and asymptotic profile, in a form similar to that of the nonlinear Schr\\\"odinger equation with supercritical power law nonlinearity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-06T20:09:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "37K40",
      "35Q51",
      "65M60"
    ],
    "keywords": [
      "derivative nonlinear schrödinger equation",
      "focusing singularity",
      "finite time singularity",
      "supercritical power law nonlinearity",
      "general power nonlinearity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.1048L"
    }
  }
}