Conservation laws and group-invariant solutions of the von Kármán equations

1996 ◽  
Vol 31 (1) ◽  
pp. 73-87 ◽  
Author(s):  
P.A. Djondjorov ◽  
V.M. Vassilev
Keyword(s):  
Conservation Laws ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Group Invariant Solutions ◽  
Von Kármán

scholarly journals Some symmetries, similarity solutions and various conservation laws of a type of dispersive water waves

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yufeng Zhang ◽  
Na Bai ◽  
Hongyang Guan
Keyword(s):  
Conservation Laws ◽  
Water Waves ◽  
Water Wave ◽  
Wave Equations ◽  
Similarity Solutions ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Lie Transformation ◽  
Group Invariant Solutions ◽  
Special Solutions

Abstract We investigate the point symmetries, Lie–Bäcklund symmetries for a type of dispersive water waves. We obtain some Lie transformation groups, various group-invariant solutions, and some similarity solutions. Besides, we produce different formats of conservation laws of the dispersive water waves by using different schemes. Finally, we consider some special solutions of the stationary dispersive water-wave equations.

scholarly journals Some invariant solutions and conservation laws of a type of long-water wave system

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiangzhi Zhang ◽  
Yufeng Zhang
Keyword(s):  
Conservation Laws ◽  
Water Wave ◽  
Lax Pair ◽  
Wave System ◽  
Series Solutions ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Generalized System ◽  
Group Invariant Solutions ◽  
Similarity Reductions

AbstractWe propose a generalized long-water wave system that reduces to the standard water wave system. We also obtain the Lax pair and symmetries of the generalized shallow-water wave system and single out some their similarity reductions, group-invariant solutions, and series solutions. We further investigate the corresponding self-adjointness and the conservation laws of the generalized system.

scholarly journals On optimal system, exact solutions and conservation laws of the modified equal-width equation

2018 ◽  
Vol 3 (2) ◽  
pp. 409-418 ◽  
Author(s):  
Chaudry Masood Khalique ◽  
Oke Davies Adeyemo ◽  
Innocent Simbanefayi
Keyword(s):  
Wave Propagation ◽  
Conservation Laws ◽  
Optimal System ◽  
Lie Point Symmetries ◽  
Invariant Solutions ◽  
Nonlinear Media ◽  
One Dimensional ◽  
Group Invariant ◽  
Group Invariant Solutions ◽  
Dimensional Wave

AbstractIn this paper we study the modified equal-width equation, which is used in handling simulation of a single dimensional wave propagation in nonlinear media with dispersion processes. Lie point symmetries of this equation are computed and used to construct an optimal system of one-dimensional subalgebras. Thereafter using an optimal system of one-dimensional subalgebras, symmetry reductions and new group-invariant solutions are presented. The solutions obtained are cnoidal and snoidal waves. Furthermore, conservation laws for the modified equal-width equation are derived by employing two different methods, the multiplier method and Noether approach.

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