Revista Matemática Iberoamericana
- Rev. Mat. Iberoamericana
- Volume 19, Number 1 (2003), 73-142.
Algebro-Geometric Solutions of the Camassa-Holm hierarchy
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.
Rev. Mat. Iberoamericana Volume 19, Number 1 (2003), 73-142.
First available in Project Euclid: 31 March 2003
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 58F07
Secondary: 35Q51: Soliton-like equations [See also 37K40]
Gesztesy, Fritz; Holden, Helge. Algebro-Geometric Solutions of the Camassa-Holm hierarchy. Rev. Mat. Iberoamericana 19 (2003), no. 1, 73--142. https://projecteuclid.org/euclid.rmi/1049123081.