On the Lie point symmetry analysis and solutions of the inviscid Burgers equation

Pramana ◽  
2011 ◽  
Vol 77 (3) ◽  
pp. 407-414 ◽  
Author(s):  
MUHAMMAD A ABDULWAHHAB ◽  
ASHFAQUE H BOKHARI ◽  
A H KARA ◽  
F D ZAMAN
Keyword(s):  
Burgers Equation ◽  
Symmetry Analysis ◽  
Point Symmetry ◽  
Inviscid Burgers Equation ◽  
Lie Point Symmetry

scholarly journals A Group Theory Approach towards Some Rational Difference Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Mensah Folly-Gbetoula ◽  
Nkosingiphile Mnguni ◽  
A. H. Kara
Keyword(s):  
Group Theory ◽  
Exact Solutions ◽  
Difference Equations ◽  
Symmetry Analysis ◽  
Point Symmetry ◽  
Theory Approach ◽  
Rational Difference Equations ◽  
Lie Point Symmetry

A full Lie point symmetry analysis of rational difference equations is performed. Nontrivial symmetries are derived, and exact solutions using these symmetries are obtained.

Symmetry analysis and some new exact solutions of some nonlinear KdV-like equations

2018 ◽  
Vol 11 (03) ◽  
pp. 1850040 ◽  
Author(s):  
A. H. Abdel Kader ◽  
M. S. Abdel Latif ◽  
F. El Bialy ◽  
A. Elsaid
Keyword(s):  
Exact Solutions ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Symmetry Analysis ◽  
Point Symmetry ◽  
New Exact Solutions ◽  
Lie Point Symmetry

In this paper, we obtained some new exact solutions of some nonlinear KdV-like equations using Lie point symmetry and [Formula: see text]-symmetry methods. The obtained solutions are in the form of doubly periodic, bright and dark soliton solutions.

scholarly journals Lie Symmetry Analysis of Burgers Equation and the Euler Equation on a Time Scale

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 10 ◽  
Author(s):  
Mingshuo Liu ◽  
Huanhe Dong ◽  
Yong Fang ◽  
Yong Zhang
Keyword(s):  
Euler Equation ◽  
Time Scale ◽  
Flow Model ◽  
Burgers Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Group Invariant ◽  
Discrete Equations ◽  
Group Invariant Solutions

As a powerful tool that can be used to solve both continuous and discrete equations, the Lie symmetry analysis of dynamical systems on a time scale is investigated. Applying the method to the Burgers equation and Euler equation, we get the symmetry of the equation and single parameter groups on a time scale. Some group invariant solutions in explicit form for the traffic flow model simulated by a Burgers equation and Euler equation with a Coriolis force on a time scale are studied.

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