{
  "id": "0812.4142",
  "version": "v1",
  "published": "2008-12-22T09:55:24.000Z",
  "updated": "2008-12-22T09:55:24.000Z",
  "title": "Painleve II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small dispersion limit",
  "authors": [
    "T. Claeys",
    "T. Grava"
  ],
  "comment": "27 pages",
  "categories": [
    "math-ph",
    "math.AP",
    "math.CA",
    "math.MP"
  ],
  "abstract": "In the small dispersion limit, solutions to the Korteweg-de Vries equation develop an interval of fast oscillations after a certain time. We obtain a universal asymptotic expansion for the Korteweg-de Vries solution near the leading edge of the oscillatory zone up to second order corrections. This expansion involves the Hastings-McLeod solution of the Painlev\\'e II equation. We prove our results using the Riemann-Hilbert approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-22T09:55:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q53",
      "33E17",
      "35Q15"
    ],
    "keywords": [
      "small dispersion limit",
      "korteweg-de vries equation",
      "oscillatory zone",
      "leading edge",
      "universal asymptotic expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.4142C"
    }
  }
}