{
  "annotation_id": "603d397a-30b6-4d00-896f-fb2d17f900e7",
  "date_created": "2026-03-02T18:00:29.366000Z",
  "date_modified": "2026-03-02T18:00:29.366000Z",
  "file_hash": "7bdbfd0f9ca61f716339c3fc5866e84f3f63c65e2082e509d709ebe37b6e3768",
  "private": false,
  "record": {
    "abstract": "Newell-Whitham type car-following model with hyperbolic tangent optimal\nvelocity function in a one-lane circuit has a finite set of the exact solutions\nfor steady traveling wave, which expressed by elliptic theta function. Each\nsolution of the set describes a density wave with definite number of\ncar-bunches in the circuit. By the numerical simulation, we observe a\ntransition process from a uniform flow to the one-bunch analytic solution,\nwhich seems to be an attractor of the system. In the process, the system shows\na series of cascade transitions visiting the configurations closely similar to\nthe higher multi-bunch solutions in the set.",
    "arxiv_id": "patt-sol/9909005",
    "authors": [
      "Ken Nakanishi"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevE.62.3349",
    "title": "Multi-Bunch Solutions of Differential-Difference Equation for Traffic   Flow",
    "url": "https://arxiv.org/abs/patt-sol/9909005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ed133fd1-8d7a-4204-997e-444cb045580a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}