{
  "id": "1604.04778",
  "version": "v1",
  "published": "2016-04-16T17:49:25.000Z",
  "updated": "2016-04-16T17:49:25.000Z",
  "title": "Free-Surface Hydrodynamics in Conformal Variables: Are Equations of Free-Surface Hydrodynamics on Deep Water Integrable?",
  "authors": [
    "Vladimir Zakharov"
  ],
  "comment": "8 pages, 7 references. The content of this article was reported on VIIIth International Lavrentyev Readings, September 6-11, 2015, Novosibirsk, Russia",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The hypothesis on complete integrability of equations describing the potential motion of incompressible ideal fluid with free surface in 2-D space in presence and absence of gravity was formulated by Dyachenko and Zakharov in 1994 [1]. Later on, the same authors found that these equations have indefinite number of additional motion constants [2] that was an argument in support of the integrability hypothesis. In this article we formulate another argument in favor of this conjecture. It is known [3] that the free-surface equations have an exotic solution that keeps the surface flat but describes the compression of the whole mass of fluid. In this article we show that the free-surface hydrodynamic is integrable if the motion can be treated as a finite amplitude perturbation of the compressed fluid solution. Integrability makes possible to construct an indefinite number of exact solutions of the Euler equations with free surface.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-16T17:49:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free-surface hydrodynamic",
      "deep water integrable",
      "conformal variables",
      "free surface",
      "indefinite number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160404778Z"
    }
  }
}