Algebro-geometric solutions of the Camassa-Holm hierarchy.

Gesztesy, Fritz, and Holden, Helge. "Algebro-geometric solutions of the Camassa-Holm hierarchy.." Revista Matemática Iberoamericana 19.1 (2003): 73-142. <http://eudml.org/doc/39687>.

@article{Gesztesy2003,
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 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.},
author = {Gesztesy, Fritz, Holden, Helge},
journal = {Revista Matemática Iberoamericana},
keywords = {Ecuación de Korteweg-de Vries; Solitones; Ecuaciones de evolución no lineales; hierarchies; soliton equations; polynomial formalism; Dubrovin-type equations; algebro-geometric initial value problem; theta function representation},
language = {eng},
number = {1},
pages = {73-142},
title = {Algebro-geometric solutions of the Camassa-Holm hierarchy.},
url = {http://eudml.org/doc/39687},
volume = {19},
year = {2003},
}

TY - JOUR
AU - Gesztesy, Fritz
AU - Holden, Helge
TI - Algebro-geometric solutions of the Camassa-Holm hierarchy.
JO - Revista Matemática Iberoamericana
PY - 2003
VL - 19
IS - 1
SP - 73
EP - 142
AB - 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.
LA - eng
KW - Ecuación de Korteweg-de Vries; Solitones; Ecuaciones de evolución no lineales; hierarchies; soliton equations; polynomial formalism; Dubrovin-type equations; algebro-geometric initial value problem; theta function representation
UR - http://eudml.org/doc/39687
ER -