English

The algebro-geometric solutions for the modified Camassa-Holm hierarchy

Exactly Solvable and Integrable Systems 2012-07-04 v2

Abstract

This paper is dedicated to provide theta function representation of algebro-geometric solutions and related crucial quantities for the modified Camassa-Holm (MCH) hierarchy through %and studying a algebro-geometric initial value problem. Our main tools include the polynomial recursive formalism to derive the MCH hierarchy, the hyperelliptic curve with finite number of genus, the Baker-Akhiezer functions, the meromorphic function, the Dubrovin-type equations for auxiliary divisors, and the associated trace formulas. With the help of these tools, the explicit representations of the Baker-Ahhiezer functions, the meromorphic function, and the algebro-geometric solutions are obtained for the entire MCH hierarchy.

Keywords

Cite

@article{arxiv.1205.6062,
  title  = {The algebro-geometric solutions for the modified Camassa-Holm hierarchy},
  author = {Yu Hou and Engui Fan and Zhijun Qiao},
  journal= {arXiv preprint arXiv:1205.6062},
  year   = {2012}
}

Comments

59 pages. arXiv admin note: text overlap with arXiv:solv-int/9809004, arXiv:solv-int/9707010, arXiv:solv-int/9707009