Algebro-Geometric Solutions of the Camassa--Holm hierarchy

Details Algebro-Geometric Solutions of the Camassa--Holm hierarchy Algebro-Geometric Solutions of the Camassa--Holm hierarchy

2001-05-08

arxiv.org/abs/nlin/0105021v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX, 52 pages, references and introduction have been updated and extended

Scientific paper

We provide a detailed treatment of the Camassa--Holm (CH) hierarchy with special emphasis on its algebro-geometric solutions. In analogy to other completely integrable hierarchies of soliton equations such as the KdV or AKNS hierarchies, the CH hierarchy is recursively constructed by means of basic polynomial formalism invoking a spectral parameter. Moreover, we study Dubrovin-type equations for auxiliary divisors and associated trace formulas, consider the corresponding algebro-geometric initial value problem, and derive the theta function representations of algebro-geometric solutions of the CH hierarchy.

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