{
  "annotation_id": "dcc14f88-b4ba-4c57-90ab-bb7bb93fa5ab",
  "date_created": "2026-03-02T18:02:51.404000Z",
  "date_modified": "2026-03-02T18:02:51.404000Z",
  "file_hash": "48820f740bb4c387f69ca6d308c757110010f9015b5050ecd77bb1bd8f3480dc",
  "private": false,
  "record": {
    "abstract": "We consider a generalization of the full symmetric Toda hierarchy where the\nmatrix $\\tilde {L}$ of the Lax pair is given by $\\tilde {L}=LS$, with a full\nsymmetric matrix $L$ and a nondegenerate diagonal matrix $S$. The key feature\nof the hierarchy is that the inverse scattering data includes a class of\nnoncompact groups of matrices, such as $O(p,q)$. We give an explicit formula\nfor the solution to the initial value problem of this hierarchy. The formula is\nobtained by generalizing the orthogonalization procedure of Szeg\\\"{o}, or the\nQR factorization method of Symes. The behaviors of the solutions are also\nstudied. Generically, there are two types of solutions, having either sorting\nproperty or blowing up to infinity in finite time. The $\\tau$-function\nstructure for the tridiagonal hierarchy is also studied.",
    "arxiv_id": "solv-int/9505004",
    "authors": [
      "Yuji Kodama",
      "Jian Ye"
    ],
    "categories": [
      "solv-int",
      "hep-th",
      "nlin.SI"
    ],
    "doi": "10.1016/0167-2789(95)00269-3",
    "title": "Toda Hierarchy with Indefinite Metric",
    "url": "https://arxiv.org/abs/solv-int/9505004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1bd4c80d-57e9-4ce7-93ef-23ed395480a2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}