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