{
  "id": "0709.3108",
  "version": "v1",
  "published": "2007-09-19T20:56:59.000Z",
  "updated": "2007-09-19T20:56:59.000Z",
  "title": "Integrable systems without the Painlevé property",
  "authors": [
    "Alfred Ramani",
    "Basile Grammaticos",
    "Sébastien Tremblay"
  ],
  "journal": "Journal of Physics A: Mathematical and General, 2000, 33, No 15, 3045-3052",
  "doi": "10.1088/0305-4470/33/15/311",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We examine whether the Painlev\\'e property is a necessary condition for the integrability of nonlinear ordinary differential equations. We show that for a large class of linearisable systems this is not the case. In the discrete domain, we investigate whether the singularity confinement property is satisfied for the discrete analogues of the non-Painlev\\'e continuous linearisable systems. We find that while these discrete systems are themselves linearisable, they possess nonconfined singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-19T20:56:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integrable systems",
      "nonlinear ordinary differential equations",
      "singularity confinement property",
      "large class",
      "possess nonconfined singularities"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2000,
      "month": "Apr",
      "volume": 33,
      "number": 15,
      "pages": 3045
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000JPhA...33.3045R"
    }
  }
}