Volume 20, Issue 2, May 2013, Pages 245 - 259
Hyperelliptic function solutions with finite genus ������ of coupled nonlinear differential equations*
Authors
Shou-Fu Tian*, ⋆, Bin Lu†, Yang Feng‡, Hong-Qing Zhang§, Chao Yang*, ⋆
*Department of Mathematics, China University of Mining and Technology, Xuzhou 221116, People's Republic of China
†School of Mathematical Sciences, Anhui University, Hefei 230601, People's Republic of China
‡School of Science, Xi'an University of Post & Telecommunications, Xi'an 710121, People's Republic of China
§School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, People's Republic of China
*
Supported by the Fundamental Research Funds for the Central Universities under the Grant No.2013QNA41.
⋆Corresponding author. sftian@cumt.edu.cn and shoufu2006@126.com (S. F. Tian)
Corresponding Authors
Shou-Fu Tian, Chao Yang
Received 22 April 2013, Accepted 27 May 2013, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2013.810406How to use a DOI?
- Keywords
- Nonlinear differential equations; Hyperelliptic function solutions; Analytic solutions
- Abstract
In this paper, using the properties of hyperelliptic σ- and ℘- functions, ℘μν : = ∂μ∂ν log σ, we propose an algorithm to obtain particular solutions of the coupled nonlinear differential equations, such as a general (2+1)- dimensional breaking soliton equation and static Veselov-Novikov(SVN) equation, the solutions of which can be expressed in terms of the hyperelliptic Kleinian functions for a given curve y2=f(x) of (2g+1)- and (2g+2)- degree with genus 𝒢. In particular, owing to the idea of CK direct method, the algorithm can generate a series of new forms of hyperelliptic function solutions with the same genus 𝒢.
- Copyright
- © 2013 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 - Shou-Fu Tian AU - Bin Lu AU - Yang Feng AU - Hong-Qing Zhang AU - Chao Yang PY - 2021 DA - 2021/01/06 TI - Hyperelliptic function solutions with finite genus ������ of coupled nonlinear differential equations* JO - Journal of Nonlinear Mathematical Physics SP - 245 EP - 259 VL - 20 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2013.810406 DO - 10.1080/14029251.2013.810406 ID - Tian2021 ER -