Abstract
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 a 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.
Citation
Fritz Gesztesy. Helge Holden. "Algebro-Geometric Solutions of the Camassa-Holm hierarchy." Rev. Mat. Iberoamericana 19 (1) 73 - 142, March, 2003.
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