{
  "annotation_id": "c2aefd09-e208-4176-924b-884517cd450b",
  "date_created": "2026-03-02T18:02:48.236000Z",
  "date_modified": "2026-03-02T18:02:48.236000Z",
  "file_hash": "130fef42485e04c70ef663269f4c5acfdcfe84577e8354de5815dcca539af681",
  "private": false,
  "record": {
    "abstract": "Classical and nonclassical symmetries of the nonlinear heat equation\n$$u_t=u_{xx}+f(u),\\eqno(1)$$ are considered. The method of differential\nGr\\\"obner bases is used both to find the conditions on $f(u)$ under which\nsymmetries other than the trivial spatial and temporal translational symmetries\nexist, and to solve the determining equations for the infinitesimals. A\ncatalogue of symmetry reductions is given including some new reductions for the\nlinear heat equation and a catalogue of exact solutions of (1) for cubic $f(u)$\nin terms of the roots of $f(u)=0$.",
    "arxiv_id": "solv-int/9306002",
    "authors": [
      "Peter A. Clarkson",
      "Elizabeth L. Mansfield"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "title": "Symmetry Reductions and Exact Solutions of a class of Nonlinear Heat   Equations",
    "url": "https://arxiv.org/abs/solv-int/9306002"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "50eedb15-67f7-4d19-a55b-584715c0e166",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}