Symmetry Reductions and New Exact Non-Traveling Wave Solutions of b -Family Equations

2017 ◽  
Vol 6 (3) ◽  
pp. 311-317
Author(s):  
M. H. M. Moussa ◽  
Zidan M. Abd Al-Halim
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Symmetry Reductions ◽  
Wave Solutions

scholarly journals Lie Symmetry Analysis, Traveling Wave Solutions, and Conservation Laws to the (3 + 1)-Dimensional Generalized B-Type Kadomtsev-Petviashvili Equation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Huizhang Yang ◽  
Wei Liu ◽  
Yunmei Zhao
Keyword(s):  
Conservation Laws ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Symmetry Reductions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Bkp Equation

In this paper, the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili(BKP) equation is studied applying Lie symmetry analysis. We apply the Lie symmetry method to the (3 + 1)-dimensional generalized BKP equation and derive its symmetry reductions. Based on these symmetry reductions, some exact traveling wave solutions are obtained by using the tanh method and Kudryashov method. Finally, the conservation laws to the (3 + 1)-dimensional generalized BKP equation are presented by invoking the multiplier method.

Symmetry Reductions and Exact Solutions to the Kudryashov–Sinelshchikov Equation

2016 ◽  
Vol 71 (11) ◽  
pp. 1059-1065 ◽  
Author(s):  
Huizhang Yang
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Explicit Solutions ◽  
Bifurcation Method ◽  
Characteristic Equations ◽  
Symmetry Reductions ◽  
Wave Solutions ◽  
Nonclassical Symmetries

AbstractIn this article, based on the compatibility method, some nonclassical symmetries of Kudryashov–Sinelshchikov equation are derived. By solving the corresponding characteristic equations associated with symmetry equations, some new exact explicit solutions of Kudryashov–Sinelshchikov equation are obtained. For the exact explicit traveling wave solutions, the exact parametric representations are investigated by the integral bifurcation method.

Traveling wave solutions of the one-dimensional Boussinesq paradigm equation

2013 ◽  
Author(s):  
V. M. Vassilev ◽  
P. A. Djondjorov ◽  
M. Ts. Hadzhilazova ◽  
I. M. Mladenov
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
One Dimensional ◽  
Wave Solutions ◽  
The One

scholarly journals Lie Group Method for Solving the Negative-Order Kadomtsev–Petviashvili Equation (nKP)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 224
Author(s):  
Ghaylen Laouini ◽  
Amr M. Amin ◽  
Mohamed Moustafa
Keyword(s):  
Lie Group ◽  
Traveling Wave ◽  
Invariant Solution ◽  
Traveling Wave Solutions ◽  
Group Method ◽  
Lie Group Method ◽  
Reduced Equations ◽  
Wave Solutions ◽  
Negative Order ◽  
Petviashvili Equation

A comprehensive study of the negative-order Kadomtsev–Petviashvili (nKP) partial differential equation by Lie group method has been presented. Initially the infinitesimal generators and symmetry reduction, which were obtained by applying the Lie group method on the negative-order Kadomtsev–Petviashvili equation, have been used for constructing the reduced equations. In particular, the traveling wave solutions for the negative-order KP equation have been derived from the reduced equations as an invariant solution. Finally, the extended improved (G′/G) method and the extended tanh method are described and applied in constructing new explicit expressions for the traveling wave solutions. Many new and more general exact solutions are obtained.

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