Journal of Nonlinear Mathematical Physics

Volume 27, Issue 4, September 2020, Pages 633 - 646

Finite genus solutions to the lattice Schwarzian Korteweg-de Vries equation

Authors
Xiaoxue Xu*
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, People’s Republic of China, xiaoxuexu@zzu.edu.cn
Cewen Cao
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, People’s Republic of China, cwcao@zzu.edu.cn
Guangyao Zhang
School of Science, Huzhou University, Zhejiang, 313000, People’s Republic of China, zgy101003@163.com
*Corresponding author.
Corresponding Author
Xiaoxue Xu
Received 22 March 2019, Accepted 25 January 2020, Available Online 4 September 2020.
DOI
https://doi.org/10.1080/14029251.2020.1819608How to use a DOI?
Keywords
lattice Schwarzian Korteweg-de Vries equation, integrable symplectic map, finite genus solution
Abstract

Based on integrable Hamiltonian systems related to the derivative Schwarzian Korteweg-de Vries (SKdV) equation, a novel discrete Lax pair for the lattice SKdV (lSKdV) equation is given by two copies of a Darboux transformation which can be used to derive an integrable symplectic correspondence. Resorting to the discrete version of Liouville-Arnold theorem, finite genus solutions to the lSKdV equation are calculated through Riemann surface method.

Copyright
© 2020 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
27 - 4
Pages
633 - 646
Publication Date
2020/09
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2020.1819608How to use a DOI?
Copyright
© 2020 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  - Xiaoxue Xu
AU  - Cewen Cao
AU  - Guangyao Zhang
PY  - 2020
DA  - 2020/09
TI  - Finite genus solutions to the lattice Schwarzian Korteweg-de Vries equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 633
EP  - 646
VL  - 27
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1819608
DO  - https://doi.org/10.1080/14029251.2020.1819608
ID  - Xu2020
ER  -