Preliminary Group Classification for One Class of Nonlinear Wave Equations

2010 ◽  
Vol 54 (2) ◽  
pp. 229-235
Author(s):  
Li Ji-Na ◽  
Zhang Ying ◽  
Zhang Shun-Li
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Group Classification ◽  
Nonlinear Wave Equations ◽  
Preliminary Group

Group classification of third order nonlinear wave equations chain’s

2020 ◽  
Vol 15 (3-4) ◽  
pp. 232-237
Author(s):  
O.K. Babkov ◽  
G.Z. Mukhametova
Keyword(s):  
Lie Algebras ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Group Analysis ◽  
Group Classification ◽  
Nonlinear Wave Equations ◽  
Bäcklund Transformations ◽  
Third Order ◽  
A Chain

The paper presents the results of point symmetrys Lie algebras for third-order nonlinear wave equations calculating linked into a chain by Bäcklund transformations. Calculations are carried out by using Lie-Ovsyannikov method of group analysis. The basic algebras of point symmetries of the indicated equations are found, all possible cases of their extension are revealed, and the commutator tables of algebras found are calculated.

scholarly journals Complete group classification of a class of nonlinear wave equations

2012 ◽  
Vol 53 (12) ◽  
pp. 123515 ◽  
Author(s):  
Alexander Bihlo ◽  
Elsa Dos Santos Cardoso-Bihlo ◽  
Roman O. Popovych
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Group Classification ◽  
Nonlinear Wave Equations ◽  
Complete Group

scholarly journals A uniqueness result for the Sine-Gordon breather

2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Rainer Mandel
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Uniqueness Result ◽  
Nonlinear Wave Equations

AbstractIn this note we prove that the sine-Gordon breather is the only quasimonochromatic breather in the context of nonlinear wave equations in $$\mathbb {R}^N$$ R N .

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