{
  "annotation_id": "1b1275aa-aa4d-4967-b503-ff614d371e4b",
  "date_created": "2026-03-02T18:00:28.668000Z",
  "date_modified": "2026-03-02T18:00:28.668000Z",
  "file_hash": "2793865763b8c546f2c795f60a8110560d13ca9c5537f313f226f9762fef71a3",
  "private": false,
  "record": {
    "abstract": "In a certain class of differential-difference equations for dissipative\nsystems, we show that hyperbolic tangent model is the only the nonlinear system\nof equations which can admit some particular solutions of the Toda lattice. We\ngive one parameter family of exact solutions, which include as special cases\nthe Toda lattice solutions as well as the Whitham\u0027s solutions in the Newell\u0027s\nmodel. Our solutions can be used to describe temporal-spatial density patterns\nobserved in the optimal velocity model for traffic flow.",
    "arxiv_id": "patt-sol/9810007",
    "authors": [
      "Yuji Igarashi",
      "Katsumi Itoh",
      "Ken Nakanishi"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1143/JPSJ.68.791",
    "title": "Toda Lattice Solutions of Differential-Difference Equations for   Dissipative Systems",
    "url": "https://arxiv.org/abs/patt-sol/9810007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d78e9012-2d2b-4219-b770-9a478b623d44",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}