{
  "annotation_id": "449b0447-c55b-4f55-a28a-2f251ff2d0bb",
  "date_created": "2026-03-02T18:02:50.571000Z",
  "date_modified": "2026-03-02T18:02:50.571000Z",
  "file_hash": "ea26c083283774bd45737571ddaba5ee84f3f0035a704649f74b6ed65c6f5a79",
  "private": false,
  "record": {
    "abstract": "The bi-Hamiltonian structure is established for the perturbation equations of\nKdV hierarchy and thus the perturbation equations themselves provide also\nexamples among typical soliton equations. Besides, a more general\nbi-Hamiltonian integrable hierarchy is proposed and a remark is given for a\ngeneralization of the resulting perturbation equations to $1+2$ dimensions.",
    "arxiv_id": "solv-int/9601003",
    "authors": [
      "Wen-Xiu Ma",
      "Benno Fuchssteiner"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1016/0375-9601(96)00112-0",
    "title": "The Bi-Hamiltonian Structure of the Perturbation Equations of KdV   Hierarchy",
    "url": "https://arxiv.org/abs/solv-int/9601003"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f35e2ce8-c5ec-422a-be17-ca6bcd15ed93",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}