Algebro-Geometric Solutions of the Camassa-Holm hierarchy

• Autores: Helge Holden, Fritz Gesztesy
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 19, Nº 1, 2003, págs. 73-142
• Idioma: inglés
• Títulos paralelos:
  • Soluciones algebro-geométricas de la jerarquía de Camassa-Holm.
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• Resumen

  • 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.