{
  "annotation_id": "b0399727-61c9-441b-a771-c249e0b91719",
  "date_created": "2026-03-02T18:02:51.387000Z",
  "date_modified": "2026-03-02T18:02:51.387000Z",
  "file_hash": "5e2f60bbb448f6b929620f4574569f5d84cdecdc9238c4f51c500dd54ed21153",
  "private": false,
  "record": {
    "abstract": "Recently the associated Camassa-Holm (ACH) equation, related to the\nFuchssteiner-Fokas-Camassa-Holm equation by a hodograph transformation, was\nintroduced by Schiff, who derived B\\\"{a}cklund transformations by a loop group\ntechnique and used these to obtain some simple soliton and rational solutions.\nWe show how the ACH equation is related to Schr\\\"{o}dinger operators and the\nKdV hierarchy, and use this connection to obtain exact solutions (rational and\nN-soliton solutions). More generally, we show that solutions of ACH on a\nconstant background can be obtained directly from the tau-functions of known\nsolutions of the KdV hierarchy on a zero background. We also present exact\nsolutions given by a particular case of the third Painlev\\\u0027{e} transcendent.",
    "arxiv_id": "solv-int/9901009",
    "authors": [
      "A. N. W. Hone"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "title": "Exact solutions of the associated Camassa-Holm equation",
    "url": "https://arxiv.org/abs/solv-int/9901009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "83db2489-979c-48ce-a7ae-d274abda6c58",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}