{
  "annotation_id": "f0d34e22-814f-481c-9499-97673fb3f82d",
  "date_created": "2026-03-02T18:02:48.585000Z",
  "date_modified": "2026-03-02T18:02:48.585000Z",
  "file_hash": "22d6f85c4839614fbe16e2288bb4eaadf173698b112fc7188c809ec644cc8c85",
  "private": false,
  "record": {
    "abstract": "By analogy to the continuous Painlev\\\u0027e II equation, we present particular\nsolutions of the discrete Painlev\\\u0027e II (d-P$\\rm_{II}$) equation. These\nsolutions are of rational and special function (Airy) type. Our analysis is\nbased on the bilinear formalism that allows us to obtain the $\\tau$ function\nfor d-P$\\rm_{II}$. Two different forms of bilinear d-P$\\rm_{II}$ are obtained\nand we show that they can be related by a simple gauge transformation.",
    "arxiv_id": "solv-int/9412007",
    "authors": [
      "J. Satsuma",
      "K. Kajiwara",
      "B. Grammaticos",
      "J. Hietarinta",
      "A. Ramani"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1088/0305-4470/28/12/025",
    "title": "Bilinear Discrete Painleve-II and its Particular Solutions",
    "url": "https://arxiv.org/abs/solv-int/9412007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "eac5828f-92ae-48b5-a2e2-0f6d65bd7fbb",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}