New exact solutions of (3 + 1)‐dimensional generalized Kadomtsev‐Petviashvili equation using a combination of lie symmetry and singular manifold methods

2019 ◽  
Vol 43 (4) ◽  
pp. 2045-2055 ◽  
Author(s):  
Rasha Saleh ◽  
Ahmed S. Rashed
Keyword(s):  
Exact Solutions ◽  
Lie Symmetry ◽  
Singular Manifold ◽  
New Exact Solutions ◽  
Petviashvili Equation

A Class of Exact Solutions of (3+1)-Dimensional Generalized B-Type Kadomtsev–Petviashvili Equation

2017 ◽  
Vol 18 (2) ◽  
pp. 137-143 ◽  
Author(s):  
Shuang Liu ◽  
Yao Ding ◽  
Jian-Guo Liu
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Traveling Wave ◽  
Expansion Method ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
New Exact Solutions ◽  
Petviashvili Equation

AbstractBy employing the generalized$(G'/G)$-expansion method and symbolic computation, we obtain new exact solutions of the (3 + 1) dimensional generalized B-type Kadomtsev–Petviashvili equation, which include the traveling wave exact solutions and the non-traveling wave exact solutions showed by the hyperbolic function and the trigonometric function. Meanwhile, some interesting physics structure are discussed.

scholarly journals Symmetry Reduction, Exact Solutions, and Conservation Laws of the ZK-BBM Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Wenbin Zhang ◽  
Jiangbo Zhou ◽  
Sunil Kumar
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Invariant Solution ◽  
Lie Symmetry ◽  
Similarity Reduction ◽  
Group Invariant ◽  
New Exact Solutions ◽  
Reduction Group ◽  
The Given ◽  
Bbm Equation

Employing the classical Lie method, we obtain the symmetries of the ZK-BBM equation. Applying the given Lie symmetry, we obtain the similarity reduction, group invariant solution, and new exact solutions. We also obtain the conservation laws of ZK-BBM equation of the corresponding Lie symmetry.

scholarly journals Lie symmetry and exact solution of (2+1)-dimensional generalized Kadomtsev-Petviashvili equation with variable coefficients

2013 ◽  
Vol 17 (5) ◽  
pp. 1490-1493
Author(s):  
Hong-Cai Ma ◽  
Zhen-Yun Qin ◽  
Ai-Ping Deng
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Variable Coefficient ◽  
Direct Method ◽  
Symmetry Transformation ◽  
Solution Procedure ◽  
Variable Coefficients ◽  
Lie Symmetry ◽  
Petviashvili Equation ◽  
Non Linear Systems

The simple direct method is adopted to find Non-Auto-Backlund transformation for variable coefficient non-linear systems. The (2+1)-dimensional generalized Kadomtsev-Petviashvili equation with variable coefficients is used as an example to elucidate the solution procedure, and its symmetry transformation and exact solutions are obtained.

Some New Exact Solutions of Jacobian Elliptic Function of Petviashvili Equation

2008 ◽  
Vol 49 (6) ◽  
pp. 1557-1560 ◽  
Author(s):  
Zhang Liang ◽  
Zhang Li-Feng ◽  
Li Chong-Yin ◽  
Wang Tie ◽  
Tan Yan-Ke
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Jacobian Elliptic Function ◽  
New Exact Solutions ◽  
Petviashvili Equation

scholarly journals Lie Symmetry Analysis and Exact Solutions of Generalized Fractional Zakharov-Kuznetsov Equations

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 601 ◽  
Author(s):  
Changzhao Li ◽  
Juan Zhang
Keyword(s):  
Exact Solutions ◽  
Vector Fields ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Point Symmetries ◽  
Lie Symmetry Analysis ◽  
Symmetry Reductions ◽  
New Exact Solutions ◽  
Symmetry Properties

This paper considers the Lie symmetry analysis of a class of fractional Zakharov-Kuznetsov equations. We systematically show the procedure to obtain the Lie point symmetries for the equation. Accordingly, we study the vector fields of this equation. Meantime, the symmetry reductions of this equation are performed. Finally, by employing the obtained symmetry properties, we can get some new exact solutions to this fractional Zakharov-Kuznetsov equation.

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