Journal of Nonlinear Mathematical Physics

Volume 26, Issue 1, December 2018, Pages 1 - 23

A hierarchy of long wave-short wave type equations: quasi-periodic behavior of solutions and their representation

Authors
Xianguo Geng, Yunyun Zhai*, Bo Xue, Jiao Wei
School of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou, Henan 450001, People’s Republic of China, xggeng@zzu.edu.cn(Xianguo Geng); zhaiyy@zzu.edu.cn(Yunyun Zhai); xuebo@zzu.edu.cn(Bo Xue); weijiaozzu@163.com(Jiao Wei)
*Corresponding authors.
Corresponding Author
Yunyun Zhai
Received 24 January 2018, Accepted 24 May 2018, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2019.1544785How to use a DOI?
Keywords
long wave-short wave type equations, Baker-Akhiezer function, meromorphic function, quasi-periodic solutions
Abstract

Based on the Lenard recursion relation and the zero-curvature equation, we derive a hierarchy of long wave-short wave type equations associated with the 3 × 3 matrix spectral problem with three potentials. Resorting to the characteristic polynomial of the Lax matrix, a trigonal curve is defined, on which the Baker-Akhiezer function and two meromorphic functions are introduced. Analyzing some properties of the meromorphic functions, including asymptotic expansions at infinite points, we obtain the essential singularities and divisor of the Baker-Akhiezer function. Utilizing the theory of algebraic curves, quasi-periodic solutions for the entire hierarchy are finally derived in terms of the Riemann theta function.

Copyright
© 2019 The Authors. Published by Atlantis 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
26 - 1
Pages
1 - 23
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2019.1544785How to use a DOI?
Copyright
© 2019 The Authors. Published by Atlantis 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  - Xianguo Geng
AU  - Yunyun Zhai
AU  - Bo Xue
AU  - Jiao Wei
PY  - 2021
DA  - 2021/01/06
TI  - A hierarchy of long wave-short wave type equations: quasi-periodic behavior of solutions and their representation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 23
VL  - 26
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2019.1544785
DO  - https://doi.org/10.1080/14029251.2019.1544785
ID  - Geng2021
ER  -