{
  "id": "1302.0148",
  "version": "v2",
  "published": "2013-02-01T11:28:41.000Z",
  "updated": "2013-07-17T09:28:10.000Z",
  "title": "Non-local Poisson structures and applications to the theory of integrable systems",
  "authors": [
    "Alberto De Sole",
    "Victor G. Kac"
  ],
  "comment": "120 pages. This paper is an edited version of the merger of the two papers with archive numbers arXiv:1210.1688 and arXiv:1211.2391. Version 2: minor corrections. Added keywords and MSC codes. To appear in the Japanese Journal of Mathematics",
  "categories": [
    "math-ph",
    "math.MP",
    "math.RA",
    "math.RT",
    "nlin.SI"
  ],
  "abstract": "We develop a rigorous theory of non-local Poisson structures, built on the notion of a non-local Poisson vertex algebra. As an application, we find conditions that guarantee applicability of the Lenard-Magri scheme of integrability to a pair of compatible non-local Poisson structures. We apply this scheme to several such pairs, proving thereby integrability of various evolution equations, as well as hyperbolic equations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-17T09:28:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37K10",
      "35Q53",
      "17B80",
      "17B69",
      "37K30",
      "17B63"
    ],
    "keywords": [
      "integrable systems",
      "application",
      "non-local poisson vertex algebra",
      "compatible non-local poisson structures",
      "evolution equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 120,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.0148D"
    }
  }
}