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.

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

Qualitative analysis for two fractional difference equations

2020 ◽  
Vol 9 (1) ◽  
pp. 265-272
Author(s):  
Mohammed B. Almatrafi ◽  
Marwa M. Alzubaidi
Keyword(s):  
Qualitative Analysis ◽  
Exact Solutions ◽  
Difference Equations ◽  
Global Attractivity ◽  
Fractional Difference ◽  
Rational Difference Equations ◽  
Fractional Difference Equations ◽  
Special Cases

AbstractSome difference equations are generally studied by investigating their long behaviours rather than their exact solutions. The proposed equations cannot be solved analytically. Hence, this article discusses the main qualitative behaviours of two rational difference equations. Some appropriate hypotheses are examined and given to show the local and global attractivity. Special cases from the considered equations are solved analytically. The periodicity is also proved in this work. We also illustrate the achieved results in some 2D figures.

Nonlocal symmetries and the nth finite symmetry transformation or AKNS system

2018 ◽  
Vol 32 (27) ◽  
pp. 1850332
Author(s):  
Xiazhi Hao ◽  
Yinping Liu ◽  
Xiaoyan Tang ◽  
Zhibin Li ◽  
Wen-Xiu Ma
Keyword(s):  
Exact Solutions ◽  
Symmetry Transformation ◽  
Original System ◽  
Point Symmetry ◽  
Auxiliary Variables ◽  
Nonlocal Symmetry ◽  
Nonlocal Symmetries ◽  
Akns System ◽  
Lie Point Symmetry ◽  
Physical Phenomena

In this paper, by introduction of pseudopotentials, the nonlocal symmetry is obtained for the Ablowitz–Kaup–Newell–Segur system, which is used to describe many physical phenomena in different applications. Together with some auxiliary variables, this kind of nonlocal symmetry can be localized to Lie point symmetry and the corresponding once finite symmetry transformation is calculated for both the original system and the prolonged system. Furthermore, the nth finite symmetry transformation represented in terms of determinant and exact solutions are derived.

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