Journal of Nonlinear Mathematical Physics

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Volume 24, Issue 1, December 2016, Pages 93 - 106

Nonlocal symmetries and conservation laws of the Sinh-Gordon equation

Authors
Xiao-yan Tang*
Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China,xytang@sist.ecnu.edu.cn
Zu-feng Liang
Department of Physics, Hangzhou Normal University, Hangzhou 310036, China,liangzufeng@163.com
*Corresponding author.
Corresponding Author
Xiao-yan Tang
Received 16 March 2016, Accepted 17 December 2016, Available Online 6 January 2021.
DOI
10.1080/14029251.2017.1282246How to use a DOI?
Keywords
Nonlocal symmetry; Nonlocal conservation law; Bäcklund transformation; Sinh-Gordon equation
Abstract

Nonlocal symmetries of the (1+1)-dimensional Sinh-Gordon (ShG) equation are obtained by requiring it, together with its Bäcklund transformation (BT), to be form invariant under the infinitesimal transformation. Naturally, the spectrum parameter in the BT enters the nonlocal symmetries, and thus through the parameter expansion procedure, infinitely many nonlocal symmetries of the ShG equation can be generated accordingly. Making advantages of the consistent conditions introduced when solving the nonlocal symmetires, some new nonlocal conservation laws of the ShG equation related to the nonlocal symmetries are obtained straightforwardly. Finally, taking the nonlocal symmetries as symmetry constraint conditions imposing on the BT, some new finite and infinite dimensional nonlinear systems are constructed.

Copyright
© 2017 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
24 - 1
Pages
93 - 106
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2017.1282246How to use a DOI?
Copyright
© 2017 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

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TY  - JOUR
AU  - Xiao-yan Tang
AU  - Zu-feng Liang
PY  - 2021
DA  - 2021/01/06
TI  - Nonlocal symmetries and conservation laws of the Sinh-Gordon equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 93
EP  - 106
VL  - 24
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2017.1282246
DO  - 10.1080/14029251.2017.1282246
ID  - Tang2021
ER  -