Non-Lie Symmetry Group and New Exact Solutions for the Two-Dimensional KdV-Burgers Equation

2011 ◽  
Vol 28 (2) ◽  
pp. 020205 ◽  
Author(s):  
Hong Wang ◽  
Ying-Hui Tian ◽  
Han-Lin Chen
Keyword(s):  
Exact Solutions ◽  
Symmetry Group ◽  
Burgers Equation ◽  
Lie Symmetry ◽  
Two Dimensional ◽  
New Exact Solutions

scholarly journals Lie symmetry group of (2+1)-dimensional Jaulent-Miodek equation

2014 ◽  
Vol 18 (5) ◽  
pp. 1547-1552
Author(s):  
Hong-Cai Ma ◽  
Ai-Ping Deng ◽  
Yao-Dong Yu
Keyword(s):  
Exact Solutions ◽  
Symmetry Group ◽  
Linear Model ◽  
Linear Models ◽  
Direct Method ◽  
Lie Symmetry ◽  
Auxiliary Equation ◽  
Auxiliary Equation Method ◽  
New Exact Solutions ◽  
Non Linear

In this paper, we consider a system of (2+1)-dimensional non-linear model by using auxiliary equation method and Clarkson-Kruskal direct method which is very important in fluid and physics. We construct some new exact solutions of (2+1)-dimensional non-linear models with the aid of symbolic computation which can illustrate some actions in fluid in the future.

scholarly journals Exact Solutions of the Two-Dimensional Cattaneo Model Using Lie Symmetry Transformations

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Khudija Bibi ◽  
Khalil Ahmad
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Lie Symmetry ◽  
Two Dimensional ◽  
Linear Combinations ◽  
Similarity Transformations ◽  
New Exact Solutions ◽  
Symmetry Transformations

In this article, symmetry technique is utilized to obtain new exact solutions of the Cattaneo equation. The infinitesimal symmetries, linear combinations of these symmetries, and corresponding similarity variables are determined, which lead to many exact solutions of the considered equation. By applying similarity transformations, the mentioned partial differential equation is reduced to some ordinary differential equations of second order. Solutions of these ordinary differential equations have yielded many exact solutions of the Cattaneo equation.

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.

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