# Symmetry Lie algebra and exact solutions of some fourth-order difference equations

Volume 11, Issue 11, pp 1262--1270 Publication Date: September 05, 2018       Article History
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### Authors

N. Mnguni - School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa. D. Nyirenda - School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa. M. Folly-Gbetoula - School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa.

### Abstract

In this paper, all the Lie point symmetries of difference equations of the form $u_{n+4}=\frac{u_n}{A_n +B_nu_nu_{n+2}},$ where, $(A_n)_{n \geq 0}$ and $(B_n)_{n \geq 0}$ are sequences of real numbers, are obtained. We perform reduction of order using the invariant of the group of transformations. Furthermore, we obtain their solutions. In particular, our work generalizes some results in the literature.

### Keywords

• Difference equation
• symmetry
• group invariant solutions

•  39A10
•  39A99
•  39A13

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