{
  "annotation_id": "8fc88a24-ca05-46c3-9ffd-79fd1207c20f",
  "date_created": "2026-03-02T18:02:51.394000Z",
  "date_modified": "2026-03-02T18:02:51.394000Z",
  "file_hash": "3e88b473625954a26c2363f1184aebe6eae012add4f7e2f60c155c885ab04316",
  "private": false,
  "record": {
    "abstract": "A straightforward algorithm for the symbolic computation of higher-order\nsymmetries of nonlinear evolution equations and lattice equations is presented.\nThe scaling properties of the evolution or lattice equations are used to\ndetermine the polynomial form of the higher-order symmetries. The coefficients\nof the symmetry can be found by solving a linear system. The method applies to\npolynomial systems of PDEs of first-order in time and arbitrary order in one\nspace variable. Likewise, lattices must be of first order in time but may\ninvolve arbitrary shifts in the discretized space variable.\n  The algorithm is implemented in Mathematica and can be used to test the\nintegrability of both nonlinear evolution equations and semi-discrete lattice\nequations. With our Integrability Package, higher-order symmetries are obtained\nfor several well-known systems of evolution and lattice equations. For PDEs and\nlattices with parameters, the code allows one to determine the conditions on\nthese parameters so that a sequence of higher-order symmetries exist. The\nexistence of a sequence of such symmetries is a predictor for integrability.",
    "arxiv_id": "solv-int/9802004",
    "authors": [
      "Unal Goktas",
      "Willy Hereman"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "title": "Computation of Higher-order Symmetries for Nonlinear Evolution and   Lattice Equations",
    "url": "https://arxiv.org/abs/solv-int/9802004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f30aad07-df66-450e-87f6-90db916c80f0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}