{
  "id": "1110.5719",
  "version": "v1",
  "published": "2011-10-26T07:20:40.000Z",
  "updated": "2011-10-26T07:20:40.000Z",
  "title": "Effective integrable dynamics for some nonlinear wave equation",
  "authors": [
    "Patrick Gerard",
    "Sandrine Grellier"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the following degenerate half wave equation on the one dimensional torus $$\\quad i\\partial_t u-|D|u=|u|^2u, \\; u(0,\\cdot)=u_0. $$ We show that, on a large time interval, the solution may be approximated by the solution of a completely integrable system-- the cubic Szeg\\\"o equation. As a consequence, we prove an instability result for large $H^s$ norms of solutions of this wave equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-26T07:20:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear wave equation",
      "effective integrable dynamics",
      "degenerate half wave equation",
      "large time interval",
      "instability result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.5719G"
    }
  }
}