## Revista Matemática Iberoamericana

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

#### 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.

#### Article information

Source
Rev. Mat. Iberoamericana Volume 19, Number 1 (2003), 73-142.

Dates
First available in Project Euclid: 31 March 2003

http://projecteuclid.org/euclid.rmi/1049123081

Mathematical Reviews number (MathSciNet)
MR1993416

Zentralblatt MATH identifier
1029.37049

#### Citation

Gesztesy, Fritz; Holden, Helge. Algebro-Geometric Solutions of the Camassa-Holm hierarchy. Rev. Mat. Iberoamericana 19 (2003), no. 1, 73--142. http://projecteuclid.org/euclid.rmi/1049123081.

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