{
  "annotation_id": "22880b27-8e32-431e-b0a5-11fbc50f88dc",
  "date_created": "2026-03-02T18:02:51.274000Z",
  "date_modified": "2026-03-02T18:02:51.274000Z",
  "file_hash": "2a12e3c1054a042d54a27a712f3fa881b1f9c84331c415579face9d6fa99fa9d",
  "private": false,
  "record": {
    "abstract": "In this paper we study the reductions of evolutionary PDEs on the manifold of\nthe stationary points of time-dependent symmetries. In particular we describe\nhow the finite dimensional Hamiltonian structure of the reduced system is\nobtained from the Hamiltonian structure of the initial PDE and we construct the\ntime-dependent Hamiltonian function. We also present a very general Lagrangian\nformulation of the procedure of reduction. As an application we consider the\ncase of the Painleve\u0027 equations PI, PII, PIII, PVI and also certain higher\norder systems appeared in the theory of Frobenius manifolds.",
    "arxiv_id": "solv-int/9902006",
    "authors": [
      "Monica Ugaglia"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "title": "On the Hamiltonian and Lagrangian structures of time-dependent   reductions of evolutionary PDEs",
    "url": "https://arxiv.org/abs/solv-int/9902006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f5c7ec06-aabf-4b51-bf0e-8d9886fa7d87",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}