{
  "annotation_id": "56096af4-a4e4-45b8-ae1a-1d8aae53e529",
  "date_created": "2026-03-02T18:02:51.155000Z",
  "date_modified": "2026-03-02T18:02:51.155000Z",
  "file_hash": "ae935b4216cd593682261b07e1477f20efea67d94151b741c984f9f00b9e0cc0",
  "private": false,
  "record": {
    "abstract": "We use the Calogero equation to illustrate the following two aspects of the\nPainleve analysis of nonlinear PDEs. First, if a nonlinear equation passes the\nPainleve test for integrability, the singular expansions of its solutions\naround characteristic hypersurfaces can be neither single-valued functions of\nindependent variables nor single-valued functionals of data. Second, if the\ntruncation of singular expansions of solutions is consistent, the truncation\nnot necessarily leads to the simplest, or elementary, auto-Backlund\ntransformation related to the Lax pair.",
    "arxiv_id": "solv-int/9909027",
    "authors": [
      "Sergei Sakovich"
    ],
    "categories": [
      "solv-int",
      "math-ph",
      "math.AP",
      "math.MP",
      "nlin.SI"
    ],
    "doi": "10.1155/2013/172813",
    "journal_ref": "Int. J. Analysis 2013 (2013) 172813 (5 pages)",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "On two aspects of the Painleve analysis",
    "url": "https://arxiv.org/abs/solv-int/9909027"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b217381e-dd77-4124-9a9c-7c4a4803e28f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}