# Invariance analysis and exact solutions of some sixth-order difference equations

Volume 10, Issue 12, pp 6262--6273
Publication Date: December 09, 2017 Submission Date: May 23, 2017
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### Authors

Darlison Nyirenda - School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa. Mensah Folly-Gbetoula - School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa.

### Abstract

We perform a full Lie point symmetry analysis of difference equations of the form $u_{n+6}=\frac{u_nu_{n+4}}{u_{n+2}(A _n + B _n u_nu_{n+4})}\ ,$ where the initial conditions are non-zero real numbers. Consequently, we obtain four non-trivial symmetries. Eventually, we get solutions of the difference equation for random sequences $(A_n)$ and $(B_n)$. This work is a generalization of a recent result by Khaliq and Elsayed [A. Khaliq, E. M. Elsayed, J. Nonlinear Sci. Appl., ${\bf 9}$ (2016), 1052--1063].

### Share and Cite

##### ISRP Style

Darlison Nyirenda, Mensah Folly-Gbetoula, Invariance analysis and exact solutions of some sixth-order difference equations, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 12, 6262--6273

##### AMA Style

Nyirenda Darlison, Folly-Gbetoula Mensah, Invariance analysis and exact solutions of some sixth-order difference equations. J. Nonlinear Sci. Appl. (2017); 10(12):6262--6273

##### Chicago/Turabian Style

Nyirenda, Darlison, Folly-Gbetoula, Mensah. "Invariance analysis and exact solutions of some sixth-order difference equations." Journal of Nonlinear Sciences and Applications, 10, no. 12 (2017): 6262--6273

### Keywords

• Difference equation
• symmetry
• group invariant solutions

•  39A10
•  39A99
•  39A13

### References

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