{
  "id": "0911.5058",
  "version": "v1",
  "published": "2009-11-26T10:54:58.000Z",
  "updated": "2009-11-26T10:54:58.000Z",
  "title": "Integrability of invariant metrics on the diffeomorphism group of the circle",
  "authors": [
    "Adrian Constantin",
    "Boris Kolev"
  ],
  "journal": "Journal of Nonlinear Science 16 (2006) 109-122",
  "doi": "10.1007/s00332-005-0707-4",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Each H^k Sobolev inner product defines a Hamiltonian vector field X_k on the regular dual of the Lie algebra of the diffeomorphism group of the circle. We show that only X_0 and X_1 are bi-Hamiltonian relatively to a modified Lie-Poisson structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-26T10:54:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "35Q53",
      "37K10",
      "37K65"
    ],
    "keywords": [
      "diffeomorphism group",
      "invariant metrics",
      "integrability",
      "sobolev inner product defines",
      "hamiltonian vector field"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of NonLinear Science",
      "year": 2006,
      "month": "Apr",
      "volume": 16,
      "number": 2,
      "pages": 109
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006JNS....16..109C"
    }
  }
}