{
  "annotation_id": "dcc5c8b9-bd60-4f16-9c4b-9b4b30c393b9",
  "date_created": "2026-03-02T18:02:50.634000Z",
  "date_modified": "2026-03-02T18:02:50.634000Z",
  "file_hash": "606fd30c8be4d7cbfb8f21ecfb1901f9e62c6af4d34e695556e5bb02209d3eed",
  "private": false,
  "record": {
    "abstract": "We derive a zero-curvature formalism for a combined sine-Gordon (sG) and\nmodified Korteweg-de Vries (mKdV) equation which yields a local sGmKdV\nhierarchy. In complete analogy to other completely integrable hierarchies of\nsoliton equations, such as the KdV, AKNS, and Toda hierarchies, the sGmKdV\nhierarchy is recursively constructed by means of a fundamental polynomial\nformalism involving a spectral parameter. We further illustrate our approach by\ndeveloping the basic algebro-geometric setting for the sGmKdV hierarchy,\nincluding Baker-Akhiezer functions, trace formulas, Dubrovin-type equations,\nand theta function representations for its algebro-geometric solutions.\nAlthough we mainly focus on sG-type equations, our formalism also yields the\nsinh-Gordon, elliptic sine-Gordon, elliptic sinh-Gordon, and Liouville-type\nequations combined with the mKdV hierarchy.",
    "arxiv_id": "solv-int/9707010",
    "authors": [
      "Fritz Gesztesy",
      "Helge Holden"
    ],
    "categories": [
      "solv-int",
      "hep-th",
      "nlin.SI"
    ],
    "title": "A combined sine-Gordon and modified Korteweg-de Vries hierarchy and its   algebro-geometric solutions",
    "url": "https://arxiv.org/abs/solv-int/9707010"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "217fb877-974a-45ff-9a23-ec063ed5050b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}