{
  "annotation_id": "b493dc54-f41a-4838-9f5d-1708f95522e6",
  "date_created": "2026-03-02T18:02:50.752000Z",
  "date_modified": "2026-03-02T18:02:50.752000Z",
  "file_hash": "28e06490093f39fc0c82b6802579ac2e50b690813bf6f4ef6b7e16906cbc48d7",
  "private": false,
  "record": {
    "abstract": "The question of constructing the finite genus quasiperiodic solutions for the\nAblowitz-Ladik hierarchy (ALH) is considered by establishing relations between\nthe ALH and the Fay\u0027s identity for the theta-functions. It is shown that using\na limiting procedure one can derive from the latter an infinite number of\ndifferential identities which can be arranged as an infinite set of\ndifferential-difference equations coinciding with the equations of the ALH, and\nthat the original Fay\u0027s identity can be rewritten in a form similar to the\nfunctional equations representing the ALH which have been derived in the\nprevious works of the author. This provides an algorithm for obtaining some\nclass of quasiperiodic solutions for the ALH, which can be viewed as an\nalternative to the inverse scattering transform or the algebro-geometrical\napproach.",
    "arxiv_id": "solv-int/9903004",
    "authors": [
      "V. E. Vekslerchik"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1088/0305-4470/32/26/316",
    "journal_ref": "Journal of Physics A, 32 (1999) 4983",
    "title": "Finite genus solutions for the Ablowitz-Ladik hierarchy",
    "url": "https://arxiv.org/abs/solv-int/9903004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8999182b-7cff-4f24-ade7-3b04f15ac5ad",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}