{
  "id": "1202.0962",
  "version": "v2",
  "published": "2012-02-05T13:52:34.000Z",
  "updated": "2012-04-20T14:53:23.000Z",
  "title": "Numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions",
  "authors": [
    "T. Grava",
    "C. Klein"
  ],
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We study numerically the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\\epsilon^{2}u_{xxx}=0$ for $\\epsilon\\ll1$ and give a quantitative comparison of the numerical solution with various asymptotic formulae for small $\\epsilon$ in the whole $(x,t)$-plane. The matching of the asymptotic solutions is studied numerically.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-20T14:53:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "small dispersion limit",
      "korteweg-de vries equation",
      "asymptotic solutions",
      "numerical study",
      "asymptotic formulae"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.physd.2012.04.001",
      "journal": "Physica D Nonlinear Phenomena",
      "year": 2012,
      "month": "Dec",
      "volume": 241,
      "number": "23-24",
      "pages": 2246
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1088298,
      "adsabs": "2012PhyD..241.2246G"
    }
  }
}