{
  "annotation_id": "17400226-0fc6-404b-9e0c-026661f71241",
  "date_created": "2026-03-02T18:02:51.407000Z",
  "date_modified": "2026-03-02T18:02:51.407000Z",
  "file_hash": "cd86805a60106e96dda802faa5e6782b6d6eace1a984857b085d73aeab9a39e2",
  "private": false,
  "record": {
    "abstract": "We suggest a generalization of the notion of invariance of a given partial\ndifferential equation with respect to Lie-B\\\"acklund vector field. Such\ngeneralization proves to be effective and enables us to construct principally\nnew Ans\\\"atze reducing evolution-type equations to several ordinary\ndifferential equations. In the framework of the said generalization we obtain\nprincipally new reductions of a number of nonlinear heat conductivity equations\n$u_t=u_{xx}+F(u,u_x)$ with poor Lie symmetry and obtain their exact solutions.\nIt is shown that these solutions can not be constructed by means of the\nsymmetry reduction procedure.",
    "arxiv_id": "solv-int/9505006",
    "authors": [
      "R. Z. Zhdanov"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1088/0305-4470/28/13/027",
    "title": "Conditional Lie-B\\\"acklund symmetry and reduction of evolution   equations.",
    "url": "https://arxiv.org/abs/solv-int/9505006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "23fccef3-82df-4eea-83ac-e960f513e7f1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}