scholarly journals Group classification of nonlinear wave equations

2005 ◽  
Vol 46 (5) ◽  
pp. 053301 ◽  
Author(s):  
V. Lahno ◽  
R. Zhdanov
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Group Classification ◽  
Nonlinear Wave Equations

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

Classification of all travelling-wave solutions for some nonlinear dispersive equations

2007 ◽  
Vol 365 (1858) ◽  
pp. 2291-2298 ◽  
Author(s):  
Jonatan Lenells
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Travelling Wave ◽  
Nonlinear Wave Equations ◽  
Dispersive Equations ◽  
Travelling Wave Solutions ◽  
Nonlinear Dispersive Equations ◽  
Wave Solutions ◽  
Wave Profiles

We present a method for the classification of all weak travelling-wave solutions for some dispersive nonlinear wave equations. When applied to the Camassa–Holm or the Degasperis–Procesi equation, the approach shows the existence of not only smooth, peaked and cusped travelling-wave solutions, but also more exotic solutions with fractal-like wave profiles.

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