{
  "annotation_id": "52a12191-1039-4f0c-ad8c-4fac3c26abb2",
  "date_created": "2026-03-02T18:02:51.398000Z",
  "date_modified": "2026-03-02T18:02:51.398000Z",
  "file_hash": "3d5f0fb3c7822a06d1fe5c78dfba7fe33868c8428c104ece0d45a905086f8713",
  "private": false,
  "record": {
    "abstract": "We study an iso-spectral deformation of general matrix which is a natural\ngeneralization of the Toda lattice equation. We prove the integrability of the\ndeformation, and give an explicit formula for the solution to the initial value\nproblem. The formula is obtained by generalizing the orthogonalization\nprocedure of Szeg\\\"{o}. Based on the root spaces for simple Lie algebras, we\nconsider several reductions of the hierarchy. These include not only the\nintegrable systems studied by Bogoyavlensky and Kostant, but also their\ngeneralizations which were not known to be integrable before. The behaviors of\nthe solutions are also studied. Generically, there are two types of solutions,\nhaving either sorting property or blowing up to infinity in finite time.",
    "arxiv_id": "solv-int/9506005",
    "authors": [
      "Yuji Kodama",
      "Jian Ye"
    ],
    "categories": [
      "solv-int",
      "hep-th",
      "nlin.SI"
    ],
    "doi": "10.1007/BF02108824",
    "title": "Iso-spectral deformations of general matrix and their reductions on Lie   algebras",
    "url": "https://arxiv.org/abs/solv-int/9506005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d0f093f9-9d50-4268-afca-51aacc21418a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}