{
  "annotation_id": "f5478cbf-abe7-4ad0-b252-ff7e1b61a146",
  "date_created": "2026-03-02T18:02:51.519000Z",
  "date_modified": "2026-03-02T18:02:51.519000Z",
  "file_hash": "49f9e1c83bc97a5983ed45c3dadc3ca188bad5e77e58a81e898403e835844c27",
  "private": false,
  "record": {
    "abstract": "We present a systematic construction of integrable third order systems based\non the coupling of an integrable second order equation and a Riccati equation.\nThis approach is the extension of the Gambier method that led to the equation\nthat bears his name. Our study is carried through for both continuous and\ndiscrete systems. In both cases the investigation is based on the study of the\nsingularities of the system (the Painlev\\\u0027e method for ODE\u0027s and the\nsingularity confinement method for mappings).",
    "arxiv_id": "solv-int/9705007",
    "authors": [
      "Stephane Lafortune",
      "Basil Grammaticos",
      "Alfred Ramani"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1088/0266-5611/14/2/005",
    "journal_ref": "Inverse Problems 14, 287-298 (1998)",
    "title": "Constructing Integrable Third Order Systems:The Gambier Approach",
    "url": "https://arxiv.org/abs/solv-int/9705007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4475c8e2-c7f1-42e6-bcba-58f447eec75e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}