1998/07/14 by Fritz Gesztesy, F. Gesztesy, H. Holden +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #nlin.SI #solv-int
paper · pdf · doi:10.48550/arxiv.solv-int/9807006
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arxiv created 1998/07/14 · openalex publication_date 1998/07/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.