Symmetry, reductions and exact solutions of the difference equation

A Group Theory Approach towards Some Rational Difference Equations

“…where the initial conditions x −5 , x −4 , x −3 , x −2 , x −1 and x 0 are arbitrary nonzero real numbers. For related work, see [2,3]. One can notice that equations (1) are just special cases of a more general form…”

“…where (a n ) n∈N 0 and (b n ) n∈N 0 are arbitrary sequences. We will use a symmetry based method to solve (2). Equivalently, we study…”

On certain sixth order difference equations

“…The method consists of finding a group of transformations that maps solutions onto themselves. Symmetry method is a valuable tool and it has been used to solve several difference equations [8,9,14,15]. In this paper, our objective is to obtain the symmetry operators of…”

On a system of second-order difference equations

“…However, calculations can be cumbersome and to the best of our knowledge, there are no computer software packages that generate symmetries for difference equations. For ideas on how to derive solutions via the symmetry approach, the reader is referred to [4,5,7,11]. Our interest is in rational ordinary difference equations, which have been researched widely using different approaches, see [1-3, 9, 14-16].…”