{
  "id": "1209.3212",
  "version": "v1",
  "published": "2012-09-14T15:03:51.000Z",
  "updated": "2012-09-14T15:03:51.000Z",
  "title": "From Vlasov-Poisson to Korteweg-de Vries and Zakharov-Kuznetsov",
  "authors": [
    "Daniel Han-Kwan"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We introduce a long wave scaling for the Vlasov-Poisson equation and derive, in the cold ions limit, the Korteweg-De Vries equation (in 1D) and the Zakharov-Kuznetsov equation (in higher dimensions, in the presence of an external magnetic field). The proofs are based on the relative entropy method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-14T15:03:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "external magnetic field",
      "cold ions limit",
      "korteweg-de vries equation",
      "vlasov-poisson equation",
      "long wave"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00220-013-1825-8",
      "journal": "Communications in Mathematical Physics",
      "year": 2013,
      "month": "Dec",
      "volume": 324,
      "number": 3,
      "pages": 961
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013CMaPh.324..961H"
    }
  }
}