{
  "annotation_id": "25eb59dd-c73f-4f9b-a82e-4312ce0ec251",
  "date_created": "2026-03-02T18:02:51.350000Z",
  "date_modified": "2026-03-02T18:02:51.350000Z",
  "file_hash": "526cfdc465853c8d477a9abdfe024500924d36d1929acc677260fde955b11853",
  "private": false,
  "record": {
    "abstract": "Polynomial-in-time dependent symmetries are analysed for polynomial-in-time\ndependent evolution equations. Graded Lie algebras, especially Virasoro\nalgebras, are used to construct nonlinear variable-coefficient evolution\nequations, both in 1+1 dimensions and in 2+1 dimensions, which possess\nhigher-degree polynomial-in-time dependent symmetries. The theory also provides\na kind of new realisation of graded Lie algebras. Some illustrative examples\nare given.",
    "arxiv_id": "solv-int/9705014",
    "authors": [
      "W. X. Ma",
      "R. K. Bullough",
      "P. J. Caudrey",
      "W. I. Fushchych"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1088/0305-4470/30/14/023",
    "title": "Time-Dependent Symmetries of Variable-Coefficient Evolution Equations   and Graded Lie Algebras",
    "url": "https://arxiv.org/abs/solv-int/9705014"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "15bbaec6-86d8-4469-bb05-bd1f1b609fbd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}