{
  "id": "1604.01092",
  "version": "v1",
  "published": "2016-04-04T23:59:57.000Z",
  "updated": "2016-04-04T23:59:57.000Z",
  "title": "Integral and asymptotic properties of solitary waves in deep water",
  "authors": [
    "Miles H. Wheeler"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider two- and three-dimensional gravity and gravity-capillary solitary water waves in infinite depth. Assuming algebraic decay rates for the free surface and velocity potential, we show that the velocity potential necessarily behaves like a dipole at infinity and obtain a related asymptotic formula for the free surface. We then prove an identity relating the \"dipole moment\" to the kinetic energy. This implies that the leading-order terms in the asymptotics are nonvanishing and in particular that the angular momentum is infinite. Lastly we prove a related integral identity which rules out waves of pure elevation or pure depression.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-04T23:59:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deep water",
      "solitary waves",
      "asymptotic properties",
      "gravity-capillary solitary water waves",
      "free surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160401092W"
    }
  }
}