Open Access
March, 2003 Algebro-Geometric Solutions of the Camassa-Holm hierarchy
Fritz Gesztesy, Helge Holden
Rev. Mat. Iberoamericana 19(1): 73-142 (March, 2003).


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.


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


Published: March, 2003
First available in Project Euclid: 31 March 2003

zbMATH: 1029.37049
MathSciNet: MR1993416

Primary: 35Q53 , 58F07
Secondary: 35Q51

Keywords: algebro-geometric solutions , Camassa-Holm hierarchy , Dubrovin equations , trace formulas

Rights: Copyright © 2003 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.19 • No. 1 • March, 2003
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