{
  "annotation_id": "cd4dc42c-8867-41f5-8f62-929833aa6f59",
  "date_created": "2026-03-02T18:02:51.296000Z",
  "date_modified": "2026-03-02T18:02:51.296000Z",
  "file_hash": "a511e514774386628489414eb7c84d1440f9779d4d930e0ad807754432b3649c",
  "private": false,
  "record": {
    "abstract": "We construct the classical Poisson structure and $r$-matrix for some finite\ndimensional integrable Hamiltonian systems obtained by constraining the flows\nof soliton equations in a certain way. This approach allows one to produce new\nkinds of classical, dynamical Yang-Baxter structures. To illustrate the method\nwe present the $r$-matrices associated with the constrained flows of the\nKaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a\n2-dimensional eigenvalue problem. Some of the obtained $r$-matrices depend only\non the spectral parameters, but others depend also on the dynamical variables.\nFor consistency they have to obey a classical Yang-Baxter-type equation,\npossibly with dynamical extra terms.",
    "arxiv_id": "solv-int/9509005",
    "authors": [
      "Yunbo Zeng",
      "Jarmo Hietarinta"
    ],
    "categories": [
      "solv-int",
      "math.QA",
      "nlin.SI",
      "q-alg"
    ],
    "doi": "10.1088/0305-4470/29/16/038",
    "title": "Classical Poisson structures and r-matrices from constrained flows",
    "url": "https://arxiv.org/abs/solv-int/9509005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "10234dab-ef19-4710-aaa3-d83f10feb75c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}