A Simplification and Generalization of Elsayed and Ibrahim’s Two-Dimensional System of Third-Order Difference Equations

Abstract

A full Lie analysis of a system of third-order difference equations is performed. Explicit solutions, expressed in terms of the initial values, are derived. Furthermore, we give sufficient conditions for the existence of two-periodic and four-periodic solutions in certain cases. Our results generalize and simplify some work in the literature.

Keywords

• symmetry
• difference equations
• exact solutions
• periodicity