{
  "id": "1903.11292",
  "version": "v1",
  "published": "2019-03-27T08:44:36.000Z",
  "updated": "2019-03-27T08:44:36.000Z",
  "title": "Solitary wave solutions of a Whitham-Bousinessq system",
  "authors": [
    "Evgueni Dinvay",
    "Dag Nilsson"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The travelling wave problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This system firstly appeared in [Dinvay, Dutykh, Kalisch 2018], where it was numerically shown to be stable and a good approximation to the incompressible Euler equations. In subsequent papers [Dinvay 2018], [Dinvay, Tesfahun 2019] the initial-value problem was studied and well-posedness in classical Sobolev spaces was proved. Here we prove existence of solitary wave solutions and provide their asymptotic description. Our proof relies on a variational approach and a concentration-compactness argument. The main difficulties stem from the fact that in the considered Euler-Lagrange equation we have a non-local operator of positive order appearing both in the linear and non-linear parts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-27T08:44:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76B15",
      "76B25",
      "35S30"
    ],
    "keywords": [
      "solitary wave solutions",
      "whitham-bousinessq system",
      "system modelling surface water waves",
      "bidirectional whitham system modelling surface",
      "whitham system modelling surface water"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}