{
  "id": "0912.2027",
  "version": "v2",
  "published": "2009-12-10T15:59:22.000Z",
  "updated": "2010-12-22T12:56:50.000Z",
  "title": "Convergence of numerical schemes for short wave long wave interaction equations",
  "authors": [
    "Paulo Amorim",
    "Mário Figueira"
  ],
  "comment": "31 pages, 7 figures",
  "doi": "10.1142/S0219891611002573",
  "categories": [
    "math.NA",
    "math.AP"
  ],
  "abstract": "We consider the numerical approximation of a system of partial differential equations involving a nonlinear Schr\\\"odinger equation coupled with a hyperbolic conservation law. This system arises in models for the interaction of short and long waves. Using the compensated compactness method, we prove convergence of approximate solutions generated by semi-discrete finite volume type methods towards the unique entropy solution of the Cauchy problem. Some numerical examples are presented.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-22T12:56:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M12",
      "35M31"
    ],
    "keywords": [
      "short wave long wave interaction",
      "wave long wave interaction equations",
      "numerical schemes",
      "convergence",
      "semi-discrete finite volume type methods"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.2027A"
    }
  }
}