Journal of Nonlinear Mathematical Physics

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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
21 - 4
Pages
473 - 508
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2014.975520How to use a DOI?
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/).

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  -