Revista Matemática Iberoamericana
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Algebro-Geometric Solutions of the Camassa–Holm hierarchyFritz Gesztesy and Helge Holden (1) Mathematics Department, University of Missouri, 202 Mathematical Sciences Bldg, MO 65211, COLUMBIA, UNITED STATES
(2) Department of Mathematical Sciences, University of Trondheim, Alfred Getz vei 1, NO-7491, TRONDHEIM, NORWAY
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.
Keywords: Camassa–Holm hierarchy, algebro-geometric solutions, Dubrovin equations, trace formulas
Gesztesy F, Holden H. Algebro-Geometric Solutions of the Camassa–Holm hierarchy. Rev. Mat. Iberoamericana 19 (2003), 73-142. doi: 10.4171/RMI/339