dorsal/arxiv
View SchemaA combined sine-Gordon and modified Korteweg-de Vries hierarchy and its algebro-geometric solutions
| Authors | Fritz Gesztesy, Helge Holden |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9707010 |
| URL | https://arxiv.org/abs/solv-int/9707010 |
Abstract
We derive a zero-curvature formalism for a combined sine-Gordon (sG) and modified Korteweg-de Vries (mKdV) equation which yields a local sGmKdV hierarchy. In complete analogy to other completely integrable hierarchies of soliton equations, such as the KdV, AKNS, and Toda hierarchies, the sGmKdV hierarchy is recursively constructed by means of a fundamental polynomial formalism involving a spectral parameter. We further illustrate our approach by developing the basic algebro-geometric setting for the sGmKdV hierarchy, including Baker-Akhiezer functions, trace formulas, Dubrovin-type equations, and theta function representations for its algebro-geometric solutions. Although we mainly focus on sG-type equations, our formalism also yields the sinh-Gordon, elliptic sine-Gordon, elliptic sinh-Gordon, and Liouville-type equations combined with the mKdV hierarchy.
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"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"
},
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"variant": "snapshot-2026-03-01",
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