{
  "annotation_id": "1365b7fc-1efe-4655-8425-f0281081c79b",
  "date_created": "2026-03-02T18:02:50.694000Z",
  "date_modified": "2026-03-02T18:02:50.694000Z",
  "file_hash": "efcb7e688f7f1de9712179d5cd79f677e437bd0886240093b2da9741e0fc9af9",
  "private": false,
  "record": {
    "abstract": "Three symbolic algorithms for testing the integrability of polynomial systems\nof partial differential and differential-difference equations are presented.\nThe first algorithm is the well-known Painlev\\\u0027e test, which is applicable to\npolynomial systems of ordinary and partial differential equations. The second\nand third algorithms allow one to explicitly compute polynomial conserved\ndensities and higher-order symmetries of nonlinear evolution and lattice\nequations.\n  The first algorithm is implemented in the symbolic syntax of both Macsyma and\nMathematica. The second and third algorithms are available in Mathematica. The\ncodes can be used for computer-aided integrability testing of nonlinear\ndifferential and lattice equations as they occur in various branches of the\nsciences and engineering. Applied to systems with parameters, the codes can\ndetermine the conditions on the parameters so that the systems pass the\nPainlev\\\u0027e test, or admit a sequence of conserved densities or higher-order\nsymmetries.",
    "arxiv_id": "solv-int/9803005",
    "authors": [
      "Willy Hereman",
      "Unal Goktas",
      "Michael D. Colagrosso",
      "Antonio J. Miller"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1016/S0010-4655(98)00121-0",
    "title": "Algorithmic Integrability Tests for Nonlinear Differential and Lattice   Equations",
    "url": "https://arxiv.org/abs/solv-int/9803005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b29a27ab-2663-45ba-8ca3-6711f3ad5a69",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}