{
  "id": "0704.0501",
  "version": "v3",
  "published": "2007-04-04T17:51:21.000Z",
  "updated": "2007-05-15T18:18:55.000Z",
  "title": "On universality of critical behaviour in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the {\\it tritronquée} solution to the Painlevé-I equation",
  "authors": [
    "B. Dubrovin",
    "T. Grava",
    "C. Klein"
  ],
  "comment": "32 pages, 10 figures",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We argue that the critical behaviour near the point of ``gradient catastrophe\" of the solution to the Cauchy problem for the focusing nonlinear Schr\\\"odinger equation $ i\\epsilon \\psi_t +\\frac{\\epsilon^2}2\\psi_{xx}+ |\\psi|^2 \\psi =0$ with analytic initial data of the form $\\psi(x,0;\\epsilon) =A(x) e^{\\frac{i}{\\epsilon} S(x)}$ is approximately described by a particular solution to the Painlev\\'e-I equation.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-05-15T18:18:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "focusing nonlinear schrödinger equation",
      "elliptic umbilic catastrophe",
      "critical behaviour",
      "painlevé-i equation",
      "tritronquée"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.0501D"
    }
  }
}