{
  "annotation_id": "70f16c99-8b64-4895-baa4-72ff41a81d58",
  "date_created": "2026-03-02T18:02:48.046000Z",
  "date_modified": "2026-03-02T18:02:48.046000Z",
  "file_hash": "fed9cfd43aa642186d969f65ce905cfa488d924ad3b88cf3700f3053061c62e8",
  "private": false,
  "record": {
    "abstract": "We give an explicit formula for the solution to the initial value problem of\nthe full symmetric Toda hierarchy. The formula is obtained by the\northogonalization procedure of Szeg\\\"{o}, and is also interpreted as a\nconsequence of the QR factorization method of Symes \\cite{symes}. The sorting\nproperty of the dynamics is also proved for the case of a generic symmetric\nmatrix in the sense described in the text, and generalizations of tridiagonal\nformulae are given for the case of matrices with $2M+1$ nonzero diagonals.",
    "arxiv_id": "solv-int/9502006",
    "authors": [
      "Y. Kodama",
      "K. T-R McLaughlin"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1007/BF00400137",
    "title": "Explicit Integration of the Full Symmetric Toda Hierarchy and the   Sorting Property",
    "url": "https://arxiv.org/abs/solv-int/9502006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b951c4ab-67e9-41e0-8021-98925c923d8f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}