# Algebro-geometric solutions of the Camassa-Holm hierarchy.

Revista Matemática Iberoamericana (2003)

- Volume: 19, Issue: 1, page 73-142
- ISSN: 0213-2230

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topGesztesy, 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 -

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