dorsal/arxiv
View SchemaDubrovin equations and integrable systems on hyperelliptic curves
| Authors | F. Gesztesy, H. Holden |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9807006 |
| URL | https://arxiv.org/abs/solv-int/9807006 |
Abstract
We introduce the most general version of Dubrovin-type equations for divisors on a hyperelliptic curve of arbitrary genus, and provide a new argument for linearizing the corresponding completely integrable flows. Detailed applications to completely integrable systems, including the KdV, AKNS, Toda, and the combined sine-Gordon and mKdV hierarchies, are made. These investigations uncover a new principle for 1+1-dimensional integrable soliton equations in the sense that the Dubrovin equations, combined with appropriate trace formulas, encode all hierarchies of soliton equations associated with hyperelliptic curves. In other words, completely integable hierarchies of soliton equations determine Dubrovin equations and associated trace formulas and, vice versa, Dubrovin-type equations combined with trace formulas permit the construction of hierarchies of soliton equations.
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"date_created": "2026-03-02T18:02:51.394000Z",
"date_modified": "2026-03-02T18:02:51.394000Z",
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"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",
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