scholarly journals Lie symmetry analysis and traveling wave solutions of equal width wave equation

2020 ◽  
Vol 39 (1) ◽  
pp. 179-198 ◽  
Author(s):  
Antim Chauhan ◽  
Rajan Arora ◽  
Amit Tomar
Keyword(s):  
Wave Equation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
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.

On the Lie symmetry analysis and traveling wave solutions of time fractional fifth-order modified Sawada-Kotera equation

2018 ◽  
pp. 411-416 ◽  
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Derivative Operator ◽  
Order Ordinary Differential Equation ◽  
Lie Group Theory ◽  
Liouville Derivative ◽  
Fifth Order

In this paper, we study Lie symmetry analysis of the time fractional fifth-order modified Sawada-Kotera equation (FMSK) with Riemann-Liouville derivative. Applying the adapted the Lie group theory to the equation under study, two dimensional Lie algebra is deduced. Using the obtained nontrivial Lie point symmetry, it is shown that the equation can be converted into a nonlinear fifth order ordinary differential equation of fractional order in the meaning of the Erdelyi-Kober fractional derivative operator. In addition, we construct some exact traveling solutions for the FMSK using the sub-equation method.

Energy-carrying wave simulation of the Lonngren-wave equation in semiconductor materials

2021 ◽  
pp. 2150213
Author(s):  
Hülya Durur
Keyword(s):  
Wave Equation ◽  
Traveling Wave ◽  
Energy Transport ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Discussion Section ◽  
Advantages And Disadvantages ◽  
Wave Solutions ◽  
Package Program

In this study, the Lonngren-wave equation, which is physically semiconductor, is taken into consideration. Traveling wave solutions of this equation are presented with generalized exponential rational function method, which is one of the mathematically powerful analytical methods. These solutions are produced in bright (non-topological) soliton and complex trigonometric-type traveling wave solutions. Three-dimensional (3D), 2D and contour graphics are presented with the help of a ready-made package program with special values given to constants in these solutions. The effect of the change in wave velocity on the traveling wave solution showing energy transport is presented with the help of simulation. It is argued that velocity is one of the important factors in wave diffraction. In the results and discussion section, the advantages and disadvantages of the method are discussed.

New soliton solutions of the CH–DP equation using Lie symmetry method

2018 ◽  
Vol 32 (20) ◽  
pp. 1850234 ◽  
Author(s):  
A. H. Abdel Kader ◽  
M. S. Abdel Latif
Keyword(s):  
Traveling Wave ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Dark Soliton ◽  
Lie Symmetry ◽  
Jacobi Elliptic Functions ◽  
Lie Symmetry Method ◽  
Wave Solutions ◽  
Symmetry Method

In this paper, using Lie symmetry method, we obtain some new exact traveling wave solutions of the Camassa–Holm–Degasperis–Procesi (CH–DP) equation. Some new bright and dark soliton solutions are obtained. Also, some new doubly periodic solutions in the form of Jacobi elliptic functions and Weierstrass elliptic functions are obtained.

scholarly journals Travelling wave solutions for a surface wave equation in fluid mechanics

2016 ◽  
Vol 20 (3) ◽  
pp. 893-898 ◽  
Author(s):  
Yi Tian ◽  
Zai-Zai Yan
Keyword(s):  
Wave Equation ◽  
Fluid Mechanics ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Linear Wave ◽  
Travelling Wave Solutions ◽  
Linear Wave Equation ◽  
Wave Solutions

This paper considers a non-linear wave equation arising in fluid mechanics. The exact traveling wave solutions of this equation are given by using G'/G-expansion method. This process can be reduced to solve a system of determining equations, which is large and difficult. To reduce this process, we used Wu elimination method. Example shows that this method is effective.

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