scholarly journals Comments on the paper “Exact solutions of nonlinear diffusion-convection-reaction equation: A Lie symmetry approach”

2021 ◽  
pp. 105922
Author(s):  
Roman Cherniha
Keyword(s):  
Exact Solutions ◽  
Nonlinear Diffusion ◽  
Lie Symmetry ◽  
Reaction Equation ◽  
Symmetry Approach ◽  
Diffusion Convection ◽  
Lie Symmetry Approach

scholarly journals Application of Lie Symmetry Analysis and Simplest Equation Method for Finding Exact Solutions of Boussinesq Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Hossein Jafari ◽  
Nematollah Kadkhoda ◽  
Chaudry Massod Khalique
Keyword(s):  
Exact Solutions ◽  
Boussinesq Equations ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Equation Method ◽  
Lie Symmetry Analysis ◽  
Symmetry Approach ◽  
Simplest Equation Method ◽  
Lie Symmetry Approach

The Lie symmetry approach with simplest equation method is used to construct exact solutions of the bad Boussinesq and good Boussinesq equations. As the simplest equation, we have used the equation of Riccati.

scholarly journals Exact Solutions ofϕ4Equation Using Lie Symmetry Approach along with the Simplest Equation and Exp-Function Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Hossein Jafari ◽  
Nematollah Kadkhoda ◽  
Chaudry Masood Khalique
Keyword(s):  
Exact Solutions ◽  
Function Method ◽  
Travelling Wave ◽  
Lie Symmetry ◽  
Equation Method ◽  
Travelling Wave Solutions ◽  
Symmetry Approach ◽  
Wave Solutions ◽  
Simplest Equation Method ◽  
Lie Symmetry Approach

This paper obtains the exact solutions of theϕ4equation. The Lie symmetry approach along with the simplest equation method and the Exp-function method are used to obtain these solutions. As a simplest equation we have used the equation of Riccati in the simplest equation method. Exact solutions obtained are travelling wave solutions.

scholarly journals Symmetry properties and exact solutions of the time fractional Kolmogorov-Petrovskii-Piskunov equation

2019 ◽  
Vol 65 (5 Sept-Oct) ◽  
pp. 529 ◽  
Author(s):  
M. S. Hasheim ◽  
M. Inc ◽  
M. Bayram
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Lie Symmetry ◽  
Conformable Fractional Derivative ◽  
Symmetry Approach ◽  
Simplest Equation Method ◽  
Symmetry Properties ◽  
Lie Symmetry Approach

In this paper, the time fractional Kolmogorov-Petrovskii-Piskunov (FKP) equation is analyzed by means of Lie symmetry approach. The FKP is reduced to ordinary differential equation of fractional order via the attained point symmetries. Moreover, the simplest equation method is used in construct the exact solutions of underlying equation with recently introduced conformable fractional derivative.

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