scholarly journals Lie Symmetry Analysis and Some New Exact Solutions for a Variable Coefficient Modified Kortweg – De Vries Equation Arising in Arterial Mechanics

2011 ◽  
Vol 11 (2) ◽  
pp. 42-48
Author(s):  
M.S. Abdel Latif ◽  
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Arterial Mechanics ◽  
New Exact Solutions ◽  
De Vries

Non-linear Dynamics and Exact Solutions for the Variable-Coefficient Modified Korteweg–de Vries Equation

2018 ◽  
Vol 73 (2) ◽  
pp. 143-149 ◽  
Author(s):  
Jiangen Liu ◽  
Yufeng Zhang
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Rational Solutions ◽  
Transformation Technique ◽  
Linear Dynamics ◽  
New Exact Solutions ◽  
Non Linear ◽  
De Vries

AbstractThis paper presents some new exact solutions which contain soliton solutions, breather solutions and two types of rational solutions for the variable-coefficient-modified Korteweg–de Vries equation, with the help of the multivariate transformation technique. Furthermore, based on these new soliton solutions, breather solutions and rational solutions, we discuss their non-linear dynamics properties. We also show the graphic illustrations of these solutions which can help us better understand the evolution of solution waves.

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.

Lie symmetry analysis and some new exact solutions of the Wu–Zhang equation

2004 ◽  
Vol 45 (1) ◽  
pp. 448 ◽  
Author(s):  
Xiaoda Ji ◽  
Chunli Chen ◽  
Jin E. Zhang ◽  
Yishen Li
Keyword(s):  
Exact Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
New Exact Solutions
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