Infinitely many nonlocal symmetries and nonlocal conservation laws of the integrable modified KdV-sine-Gordon equation

2021 ◽  
Author(s):  
Zufeng Liang ◽  
Xiao-yan Tang ◽  
Wei Ding
Keyword(s):  
Conservation Laws ◽  
Gordon Equation ◽  
Sine Gordon Equation ◽  
Nonlocal Symmetries ◽  
Nonlocal Conservation Laws

scholarly journals Nonlocal Conservation Laws of PDEs Possessing Differential Coverings

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1760
Author(s):  
Iosif Krasil’shchik
Keyword(s):  
Conservation Laws ◽  
Conservation Law ◽  
Gordon Equation ◽  
Bäcklund Transformation ◽  
General Nature ◽  
Backlund Transformation ◽  
Sine Gordon Equation ◽  
Modern Language ◽  
Nonlocal Conservation Laws

In his 1892 paper, L. Bianchi noticed, among other things, that quite simple transformations of the formulas that describe the Bäcklund transformation of the sine-Gordon equation lead to what is called a nonlocal conservation law in modern language. Using the techniques of differential coverings, we show that this observation is of a quite general nature. We describe the procedures to construct such conservation laws and present a number of illustrative examples.

Conservation Laws in sine-Gordon Equation

2003 ◽  
Vol 20 (7) ◽  
pp. 1003-1005 ◽  
Author(s):  
Shi Li-Na ◽  
Cai Hao ◽  
Li Cheng-Fang ◽  
Huang Nian-Ning
Keyword(s):  
Conservation Laws ◽  
Gordon Equation ◽  
Sine Gordon Equation

Symmetries of generalized Klein-Gordon (including sine-Gordon) equations in three or more dimensions

1987 ◽  
Vol 101 (2) ◽  
pp. 343-348 ◽  
Author(s):  
T. J. Gordon
Keyword(s):  
Conservation Laws ◽  
Gordon Equation ◽  
Nonlinear Partial Differential Equations ◽  
Higher Dimensions ◽  
Higher Order ◽  
Two Dimensional ◽  
Sine Gordon Equation ◽  
Klein Gordon ◽  
Image Position ◽  
Recent Attention

Much recent attention has been devoted to those nonlinear partial differential equations admitting higher-order conservation laws (e.g. [2] and references therein) or equivalently admitting higher-order symmetries. In particular the sine-Gordon equation possesses such symmetries [5, 7] where is the two-dimensional d'Alembertian operator. The question posed and solved here is whether such behaviour is possible in higher dimensions. We therefore consider the ‘Generalized Klein–Gordon’ (GKG) equationin N dimensions where and N ≥ 3.

Symmetries of generalized Klein–Gordon (including sine-Gordon) equations in two dimensions

1987 ◽  
Vol 102 (3) ◽  
pp. 573-586
Author(s):  
T. J. Gordon
Keyword(s):  
Conservation Laws ◽  
Gordon Equation ◽  
Two Dimensions ◽  
Sine Gordon Equation ◽  
Fundamental Significance ◽  
Klein Gordon ◽  
Countably Infinite ◽  
Infinite Set

Much attention has been devoted over the years to the sine-Gordon equation φuv = sin φ (e.g. [2] and references therein). Of fundamental significance is the existence of a countably infinite set of conservation laws, which arises from a corresponding set of symmetries (e.g. [6, 7]).

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