Algebro-geometric solutions for the two-component Hunter-Saxton hierarchy
Abstract
This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the two-component Hunter-Saxton (HS2) hierarchy through studying an algebro-geometric initial value problem. Our main tools include the polynomial recursive formalism, 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 algebro-geometric solutions are obtained for the entire HS2 hierarchy.
Keywords
Cite
@article{arxiv.1406.6359,
title = {Algebro-geometric solutions for the two-component Hunter-Saxton hierarchy},
author = {Yu Hou and Engui Fan},
journal= {arXiv preprint arXiv:1406.6359},
year = {2015}
}
Comments
46 pages. accepted for publication J Nonl Math Phys, 2014. arXiv admin note: substantial text overlap with arXiv:1406.6153, arXiv:1207.0574, arXiv:1205.6062; and with arXiv:nlin/0105021 by other authors