scholarly journals Optimal system, nonlinear self-adjointness and conservation laws for generalized shallow water wave equation

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 364-370 ◽  
Author(s):  
Dumitru Baleanu ◽  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Aliyu Isa Aliyu
Keyword(s):  
Exact Solution ◽  
Wave Equation ◽  
Conservation Laws ◽  
Shallow Water ◽  
Water Wave ◽  
Airy Function ◽  
One Dimensional ◽  
Shallow Water Wave ◽  
Differential Substitution ◽  
Conservation Theorem

AbstractIn this article, the generalized shallow water wave (GSWW) equation is studied from the perspective of one dimensional optimal systems and their conservation laws (Cls). Some reduction and a new exact solution are obtained from known solutions to one dimensional optimal systems. Some of the solutions obtained involve expressions with Bessel function and Airy function [1,2,3]. The GSWW is a nonlinear self-adjoint (NSA) with the suitable differential substitution, Cls are constructed using the new conservation theorem.

Group properties and conservation laws for nonlocal shallow water wave equation

2011 ◽  
Vol 218 (3) ◽  
pp. 974-979 ◽  
Author(s):  
Farshad Rezvan ◽  
Emrullah Yaşar ◽  
Teoman Özer
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Shallow Water ◽  
Water Wave ◽  
Shallow Water Wave

scholarly journals Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1439
Author(s):  
Chaudry Masood Khalique ◽  
Karabo Plaatjie
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Elliptic Integral ◽  
Momentum Conservation ◽  
Two Dimensional ◽  
Order Ordinary Differential Equation ◽  
Closed Form Solutions ◽  
Shallow Water Wave

In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained and solved in terms of an incomplete elliptic integral. Moreover, with the aid of Kudryashov’s approach, more closed-form solutions are constructed. In addition, energy and linear momentum conservation laws for the underlying equation are computed by engaging the multiplier approach as well as Noether’s theorem.

scholarly journals On a shallow water wave equation

Nonlinearity ◽  
1994 ◽  
Vol 7 (3) ◽  
pp. 975-1000 ◽  
Author(s):  
P A Clarkson ◽  
E L Mansfield
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Shallow Water Wave
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