{
  "annotation_id": "1e090811-b075-495d-a66c-7f4025c7c737",
  "date_created": "2026-03-02T18:02:50.969000Z",
  "date_modified": "2026-03-02T18:02:50.969000Z",
  "file_hash": "bf1637ccc19b953842279ffb55f4c5e828f6addb00b6305ee70271a7a0888d60",
  "private": false,
  "record": {
    "abstract": "Group theoretical methods are used to study the equations describing\n\\chi^{(2)}:\\chi^{(2)} cascading. The equations are shown not to be integrable\nby inverse scattering techniques. On the other hand, these equations do share\nsome of the nice properties of soliton equations. Large families of explicit\nanalytical solutions are obtained in terms of elliptic functions. In special\ncases, these periodic solutions reduce to localized ones, i.e., solitary waves.\nAll previously known explicit solutions are recovered, and many additional ones\nare obtained",
    "arxiv_id": "solv-int/9812013",
    "authors": [
      "S. Lafortune",
      "P. Winternitz",
      "C. R. Menyuk"
    ],
    "categories": [
      "solv-int",
      "nlin.SI",
      "physics.optics"
    ],
    "doi": "10.1103/PhysRevE.58.2518",
    "journal_ref": "Physical Review E 58, 2518-2825 (1998)",
    "title": "Solutions to the Optical Cascading Equations",
    "url": "https://arxiv.org/abs/solv-int/9812013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "863ec56d-8ce0-423f-bba3-5e0131c01d5c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}