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Volume 21, Issue 4, October 2014, Pages 473 - 508
Algebro-geometric solutions for the two-component Hunter-Saxton hierarchy
Authors
Yu Hou
School of Mathematical Sciences, Institute of Mathematics and Key Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai 200433, P.R. China
Engui Fan*
School of Mathematical Sciences, Institute of Mathematics and Key Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai 200433, P.R. China
*Corresponding author: faneg@fudan.edu.cn
Corresponding Author
Engui Fan
Received 5 April 2014, Accepted 29 May 2014, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2014.975520How to use a DOI?
- Keywords
- Hyperelliptic curve; Baker-Akhiezer function; Algebro-geometric solutions; Trace formulas
- 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 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.
- Copyright
- © 2014 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
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Cite this article
TY - JOUR AU - Yu Hou AU - Engui Fan PY - 2021 DA - 2021/01/06 TI - Algebro-geometric solutions for the two-component Hunter-Saxton hierarchy JO - Journal of Nonlinear Mathematical Physics SP - 473 EP - 508 VL - 21 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2014.975520 DO - 10.1080/14029251.2014.975520 ID - Hou2021 ER -