scholarly journals Lie symmetry analysis and conservation law for the equation arising from higher order Broer-Kaup equation

2019 ◽  
Vol 17 (1) ◽  
pp. 1045-1054
Author(s):  
Hengtai Wang ◽  
Huiwen Chen ◽  
Zigen Ouyang ◽  
Fubin Li
Keyword(s):  
Lie Group ◽  
Conservation Law ◽  
Higher Order ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Group Method ◽  
Lie Symmetry Analysis ◽  
Lie Group Method ◽  
Similarity Reductions

Abstract In this paper, Lie symmetry analysis is performed for the equation derived from $(2+1)$-dimensional higher order Broer-Kaup equation. Meanwhile, the optimal system and similarity reductions based on the Lie group method are obtained. Furthermore, the conservation law is studied via the Ibragimov’s method.

scholarly journals Lie Symmetry Analysis, Self-Adjointness and Conservation Law for a Type of Nonlinear Equation

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1313
Author(s):  
Hengtai Wang ◽  
Zhiwei Zou ◽  
Xin Shen
Keyword(s):  
Nonlinear Equation ◽  
Lie Group ◽  
Conservation Law ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Group Method ◽  
Lie Symmetry Analysis ◽  
Lie Group Method ◽  
The Given ◽  
Similarity Reductions

In the present paper, we mainly focus on the symmetry of the solutions of a given PDE via Lie group method. Meanwhile we transfer the given PDE to ODEs by making use of similarity reductions. Furthermore, it is shown that the given PDE is self-adjoining, and we also study the conservation law via multiplier approach.

scholarly journals Symmetry Analysis and Conservation Laws of a Generalized Two-Dimensional Nonlinear KP-MEW Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Khadijo Rashid Adem ◽  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Expansion Method ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Two Dimensional ◽  
Lie Symmetry Analysis ◽  
One Dimensional ◽  
Similarity Reductions

Lie symmetry analysis is performed on a generalized two-dimensional nonlinear Kadomtsev-Petviashvili-modified equal width equation. The symmetries and adjoint representations for this equation are given and an optimal system of one-dimensional subalgebras is derived. The similarity reductions and exact solutions with the aid ofG′/G-expansion method are obtained based on the optimal systems of one-dimensional subalgebras. Finally conservation laws are constructed by using the multiplier method.

scholarly journals SYMMETRY ANALYSIS OF TELEGRAPH EQUATION

2011 ◽  
Vol 04 (01) ◽  
pp. 117-126
Author(s):  
Mehdi Nadjafikhah ◽  
Seyed-Reza Hejazi
Keyword(s):  
Symmetry Group ◽  
Lie Algebra ◽  
Telegraph Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Group Method ◽  
Parameter Group ◽  
One Dimensional

Lie symmetry group method is applied to study the telegraph equation. The symmetry group and one-parameter group associated to the symmetries with the structure of the Lie algebra symmetries are determined. The reduced version of equation and its one-dimensional optimal system are given.

Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham–Broer–Kaup–Like Equations

2017 ◽  
Vol 72 (3) ◽  
pp. 269-279 ◽  
Author(s):  
Xiu-Bin Wang ◽  
Shou-Fu Tian ◽  
Chun-Yan Qin ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Vector Fields ◽  
Wave Equations ◽  
Boussinesq Equations ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Lie Symmetry Analysis ◽  
Bidirectional Propagation

AbstractIn this article, a generalised Whitham–Broer–Kaup–Like (WBKL) equations is investigated, which can describe the bidirectional propagation of long waves in shallow water. The equations can be reduced to the dispersive long wave equations, variant Boussinesq equations, Whitham–Broer–Kaup–Like equations, etc. The Lie symmetry analysis method is used to consider the vector fields and optimal system of the equations. The similarity reductions are given on the basic of the optimal system. Furthermore, the power series solutions are derived by using the power series theory. Finally, based on a new theorem of conservation laws, the conservation laws associated with symmetries of this equations are constructed with a detailed derivation.

scholarly journals Exact Solutions and Conservation Laws of the (3 + 1)-Dimensional B-Type Kadomstev–Petviashvili (BKP)-Boussinesq Equation

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 97 ◽  
Author(s):  
Ben Gao ◽  
Yao Zhang
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Boussinesq Equation ◽  
Lie Symmetry ◽  
Optimal System ◽  
Lie Symmetry Analysis ◽  
One Dimensional ◽  
Reduced Equations ◽  
Tanh Method ◽  
Similarity Reductions

In this paper, Lie symmetry analysis is presented for the (3 + 1)-dimensional BKP-Boussinesq equation, which seriously affects the dispersion relation and the phase shift. To start with, we derive the Lie point symmetry and construct the optimal system of one-dimensional subalgebras. Moreover, according to the optimal system, similarity reductions are investigated and we obtain exact solutions of reduced equations by means of the Tanh method. In the end, we establish conservation laws using Ibragimov’s approach.

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