Algebro-Geometric Solutions of the Camassa-Holm hierarchy
Gesztesy, Fritz ; Holden, Helge
Rev. Mat. Iberoamericana, Tome 19 (2003) no. 2, p. 73-142 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 2003-03-15
Classification:  Camassa-Holm hierarchy,  algebro-geometric solutions,  Dubrovin equations,  trace formulas,  35Q53,  58F07,  35Q51 
@article{1049123081,
     author = {Gesztesy, Fritz and Holden, Helge},
     title = {Algebro-Geometric Solutions of the Camassa-Holm hierarchy},
     journal = {Rev. Mat. Iberoamericana},
     volume = {19},
     number = {2},
     year = {2003},
     pages = { 73-142},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1049123081}
}

Gesztesy, Fritz; Holden, Helge. Algebro-Geometric Solutions of the Camassa-Holm hierarchy. Rev. Mat. Iberoamericana, Tome 19 (2003) no. 2, pp.  73-142. http://gdmltest.u-ga.fr/item/1049123081/