{
  "id": "0911.5686",
  "version": "v1",
  "published": "2009-11-30T16:40:24.000Z",
  "updated": "2009-11-30T16:40:24.000Z",
  "title": "Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit",
  "authors": [
    "T. Claeys",
    "T. Grava"
  ],
  "comment": "25 pages, 4 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\\epsilon^{2}u_{xxx}=0$ in a critical scaling regime where $x$ approaches the trailing edge of the region where the KdV solution shows oscillatory behavior. Using the Riemann-Hilbert approach, we obtain an asymptotic expansion for the KdV solution in a double scaling limit, which shows that the oscillations degenerate to sharp pulses near the trailing edge. Locally those pulses resemble soliton solutions of the KdV equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-30T16:40:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q53",
      "35Q15"
    ],
    "keywords": [
      "small dispersion limit",
      "korteweg-de vries equation",
      "solitonic asymptotics",
      "kdv solution",
      "pulses resemble soliton solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.5686C"
    }
  }
}