{
  "id": "1303.6721",
  "version": "v1",
  "published": "2013-03-27T01:40:03.000Z",
  "updated": "2013-03-27T01:40:03.000Z",
  "title": "Global bifurcation for the Whitham equation",
  "authors": [
    "Mats Ehrnstrom",
    "Henrik Kalisch"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove the existence of a global bifurcation branch of $2\\pi$-periodic, smooth, traveling-wave solutions of the Whitham equation. It is shown that any subset of solutions in the global branch contains a sequence which converges uniformly to some solution of H\\\"older class $C^{\\alpha}$, $\\alpha < \\frac{1}{2}$. Bifurcation formulas are given, as well as some properties along the global bifurcation branch. In addition, a spectral scheme for computing approximations to those waves is put forward, and several numerical results along the global bifurcation branch are presented, including the presence of a turning point and a `highest', cusped wave. Both analytic and numerical results are compared to traveling-wave solutions of the KdV equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-27T01:40:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q53",
      "35C07",
      "45K05",
      "76B15",
      "76B25"
    ],
    "keywords": [
      "whitham equation",
      "global bifurcation branch",
      "traveling-wave solutions",
      "global branch contains",
      "numerical results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.6721E"
    }
  }
}