Journal of Nonlinear Mathematical Physics

Volume 27, Issue 4, September 2020, Pages 581 - 591

Nonlocal symmetries and group invariant solutions for the coupled variable-coefficient Newell-Whitehead system

Authors
Yarong Xia
School of Computer Science, Shaanxi Normal University, Xi’an, Shaanxi, 710119, People’s Republic of China
School of Information and Engineering, Shaanxi Joint Laboratory for Artificial Intelligence, Xi’an University, Xi’an, Shaanxi, 710065, People’s Republic of China, xiayarong2014@126.com
Ruoxia Yao*
School of Computer Science, Shaanxi Normal University, Xi’an, Shaanxi, 710119, People’s Republic of China, rxyao2@hotmail.com
Xiangpeng Xin
School of Mathematical Sciences, Liaocheng University, Liaocheng, Shandong, 252059, People’s Republic of China, xinxiangpeng2012@gmail.com
*Corresponding author.
Corresponding Author
Ruoxia Yao
Received 18 July 2019, Accepted 3 January 2020, Available Online 4 September 2020.
DOI
https://doi.org/10.1080/14029251.2020.1819601How to use a DOI?
Keywords
Nonlocal symmetry, Group invariant solution, Lie point symmetry, Symmetry reduction, Variable-coefficient Newell-Whitehead system
Abstract

Starting from the Lax pairs, the nonlocal symmetries of the coupled variable-coefficient Newell-Whitehead system are obtained. By introducing an appropriate auxiliary dependent variable, the nonlocal symmetries are localized to Lie point symmetries and the coupled variable-coefficient Newell-Whitehead system is extended to an enlarged system with the auxiliary variable. Then the finite symmetry transformation for the prolonged system is found by solving the initial-value problems. Furthermore, by applying symmetry reduction method to the enlarged system, two kinds of the group invariant solutions are given.

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
581 - 591
Publication Date
2020/09
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2020.1819601How 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  - Yarong Xia
AU  - Ruoxia Yao
AU  - Xiangpeng Xin
PY  - 2020
DA  - 2020/09
TI  - Nonlocal symmetries and group invariant solutions for the coupled variable-coefficient Newell-Whitehead system
JO  - Journal of Nonlinear Mathematical Physics
SP  - 581
EP  - 591
VL  - 27
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1819601
DO  - https://doi.org/10.1080/14029251.2020.1819601
ID  - Xia2020
ER  -