{
  "annotation_id": "05a77ede-503f-4275-97d7-a623f9f8bd04",
  "date_created": "2026-03-02T18:02:51.394000Z",
  "date_modified": "2026-03-02T18:02:51.394000Z",
  "file_hash": "dcff6287a088f9d9a683151ab3a84be89b7ffb88bf2d35b47a5cb75dd1c0414d",
  "private": false,
  "record": {
    "abstract": "We introduce the most general version of Dubrovin-type equations for divisors\non a hyperelliptic curve of arbitrary genus, and provide a new argument for\nlinearizing the corresponding completely integrable flows. Detailed\napplications to completely integrable systems, including the KdV, AKNS, Toda,\nand the combined sine-Gordon and mKdV hierarchies, are made. These\ninvestigations uncover a new principle for 1+1-dimensional integrable soliton\nequations in the sense that the Dubrovin equations, combined with appropriate\ntrace formulas, encode all hierarchies of soliton equations associated with\nhyperelliptic curves. In other words, completely integable hierarchies of\nsoliton equations determine Dubrovin equations and associated trace formulas\nand, vice versa, Dubrovin-type equations combined with trace formulas permit\nthe construction of hierarchies of soliton equations.",
    "arxiv_id": "solv-int/9807006",
    "authors": [
      "F. Gesztesy",
      "H. Holden"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "title": "Dubrovin equations and integrable systems on hyperelliptic curves",
    "url": "https://arxiv.org/abs/solv-int/9807006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6d2c7d8b-3103-4fdd-9903-4056f1921aaf",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}