{
  "annotation_id": "91d6da9f-e681-47fa-b76e-ec9c757e51e9",
  "date_created": "2026-03-02T18:00:28.606000Z",
  "date_modified": "2026-03-02T18:00:28.606000Z",
  "file_hash": "5281035acb84711eeb87ca3bf8ef35f0ee6cf1f60c58ce98c6967817b494a09b",
  "private": false,
  "record": {
    "abstract": "We study parametric resonance of interacting waves having the same wave\nvector and frequency. In addition to the well-known period-doubling instability\nwe show that under certain conditions the instability is caused by a Hopf\nbifurcation leading to quasiperiodic traveling waves. It occurs, for example,\nif the group velocities of both waves have different signs and the damping is\nweak. The dynamics above the threshold is briefly discussed. Examples\nconcerning ferromagnetic spin waves and surface waves of ferro fluids are\ndiscussed.",
    "arxiv_id": "patt-sol/9605006",
    "authors": [
      "Franz-Josef Elmer"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevLett.77.179",
    "journal_ref": "Phys. Rev. Lett., 77 (1996) 179",
    "title": "Direct Hopf Bifurcation in Parametric Resonance of Hybridized Waves",
    "url": "https://arxiv.org/abs/patt-sol/9605006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9f014c9d-ed77-4203-88a4-c2d4f0f3b896",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}