Algebro-Geometric Solutions of the Camassa--Holm hierarchy
Exactly Solvable and Integrable Systems
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.nlin/0105021,
title = {Algebro-Geometric Solutions of the Camassa--Holm hierarchy},
author = {Fritz Gesztesy and Helge Holden},
journal= {arXiv preprint arXiv:nlin/0105021},
year = {2007}
}
Comments
LaTeX, 52 pages, references and introduction have been updated and extended