scholarly journals New nonlocal symmetries and conservation laws of the (1+1)-dimensional Sine-Gordon equation

2014 ◽  
Vol 490 ◽  
pp. 012032 ◽  
Author(s):  
Zufeng Liang ◽  
Xiaoyan Tang ◽  
Senyue Lou
Keyword(s):  
Conservation Laws ◽  
Gordon Equation ◽  
Sine Gordon Equation ◽  
Nonlocal Symmetries

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]).

On polynomial symmetries of the sine-Gordon equation

1982 ◽  
Vol 91 (3) ◽  
pp. 485-489 ◽  
Author(s):  
G. Z. Tu
Keyword(s):  
Conservation Laws ◽  
Gordon Equation ◽  
Soliton Solutions ◽  
Sine Gordon Equation ◽  
Soliton Theory ◽  
Sg Equation

The sine-Gordon (SG) equation uxt = sin u arises from many branches of physics, and now is one of the most important equations in soliton theory. There have been many works concerning its soliton solutions, Backhand transformations, symmetries and conservation laws and other properties. In this paper we prove that every polynomial symmetry of the SG equation is Hamiltonian, that is, takes the form of D-l δh/δu.

scholarly journals Liouville Correspondence Between the Short-Pulse Hierarchy and the Sine-Gordon Hierarchy

2016 ◽  
Vol 71 (12) ◽  
pp. 1111-1120
Author(s):  
Jing Kang ◽  
Xiaochuan Liu ◽  
Changzheng Qu
Keyword(s):  
Conservation Laws ◽  
Gordon Equation ◽  
Short Pulse ◽  
Integrable Hierarchy ◽  
Sine Gordon Equation ◽  
Short Pulse Equation ◽  
Alternative Approach

AbstractThe Liouville correspondence between the short-pulse integrable hierarchy and the sine-Gordon integrable hierarchy is studied. It is shown that the transformation relating the short-pulse equation with the sine-Gordon equation also establishes the correspondence between their flows and Hamiltonian conservation laws in respective hierarchy. This proposes an alternative approach to derive the Hamiltonian conservation laws of the short-pulse equation from the known ones of the classical sine-Gordon equation.

Conservation laws of sine-Gordon equation

1974 ◽  
Vol 48 (3) ◽  
pp. 221-222 ◽  
Author(s):  
H. Sanuki ◽  
K. Konno
Keyword(s):  
Conservation Laws ◽  
Gordon Equation ◽  
Sine Gordon Equation
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