Nonlocal symmetries and conservation laws of the Sinh-Gordon equation
- 10.1080/14029251.2017.1282246How to use a DOI?
- Nonlocal symmetry; Nonlocal conservation law; Bäcklund transformation; Sinh-Gordon equation
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.
- © 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
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 -