{
  "annotation_id": "4198a0dd-8bb6-4ba2-8116-04283a4528b7",
  "date_created": "2026-03-02T18:02:50.634000Z",
  "date_modified": "2026-03-02T18:02:50.634000Z",
  "file_hash": "b8aabef7a28cce5ccc22edbe8db2c38674b36dc4ad8da0512fb630efd479e38b",
  "private": false,
  "record": {
    "abstract": "Scaling similarity solutions of three integrable PDEs, namely the\nSawada-Kotera, fifth order KdV and Kaup-Kupershmidt equations, are considered.\nIt is shown that the resulting ODEs may be written as non-autonomous\nHamiltonian equations, which are time-dependent generalizations of the\nwell-known integrable H\\\u0027{e}non-Heiles systems. The (time-dependent)\nHamiltonians are given by logarithmic derivatives of the tau-functions\n(inherited from the original PDEs). The ODEs for the similarity solutions also\nhave inherited B\\\"{a}cklund transformations, which may be used to generate\nsequences of rational solutions as well as other special solutions related to\nthe first Painlev\\\u0027{e} transcendent.",
    "arxiv_id": "solv-int/9703005",
    "authors": [
      "Andrew N. W. Hone"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1016/S0167-2789(98)00010-4",
    "title": "Non-autonomous H\\\u0027{e}non-Heiles Systems",
    "url": "https://arxiv.org/abs/solv-int/9703005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "25cb2bdb-d651-4af5-a6d5-4450e4b99b96",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}