Fritz Gesztesy and Helge Holden
Algebro-Geometric Solutions of the Camassa--Holm Hierarchy
(174K, LaTeX)
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
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.