{
  "annotation_id": "8168d9e1-4179-4c4f-886b-d20f46964e65",
  "date_created": "2026-03-02T18:02:51.400000Z",
  "date_modified": "2026-03-02T18:02:51.400000Z",
  "file_hash": "2e35857b88b20162c746f3d0a3b3a566225eccaf4b95aaa15015f176eb80a601",
  "private": false,
  "record": {
    "abstract": "There are considered differential substitutions of the form $v=P(x,u,u_{x})$\nfor which there exists a differential operator $H=\\sum^{k}_{i=0} \\alpha_{i}\nD^{i}_{x}$ such that the differential substitution maps the equation\n$u_{t}=H[s(x,P,D_{x}(P),...,D^{k}_{x}(P))]$ into an evolution equation for any\nfunction $s$ and any nonnegative integer $k$. All differential substitutions of\nthe form $v=P(x,u,u_{x})$ known to the author have this property. For example,\nthe well-known Miura transformation $v=u_{x}-u^{2}$ maps any equation of the\nform $$u_{t}=(D^{2}_{x}+2uD_{x}+2u_{x})\n[s(x,u_{x}-u^{2},D_{x}(u_{x}-u^{2}),...,D^{k}_{x}(u_{x}-u^{2}))]$$ into the\nequation $$v_{t}=(D^{3}_{x}+4vD_{x}+2v_{x})[s(x,v,{{\\partial v}\\over{\\partial x\n}},...,{{\\partial^{k} v}\\over{\\partial x^{k}}})].$$ The complete classification\nof such differential substitutions is given. An infinite set of the pairwise\nnonequivalent differential substitutions with the property mentioned above is\nconstructed. Moreover, a general result about symmetries and invariant\nfunctions of hyperbolic equations is obtained.",
    "arxiv_id": "solv-int/9509006",
    "authors": [
      "S. Ya. Startsev"
    ],
    "categories": [
      "solv-int",
      "nlin.PS",
      "nlin.SI",
      "patt-sol"
    ],
    "title": "Differential substitutions and symmetries of hyperbolic equations",
    "url": "https://arxiv.org/abs/solv-int/9509006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a5f3e55a-0bbb-4d44-afd1-51e048df4ff9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}