Symmetries and exact solutions of systems of ordinary difference equations

Abstract

In this dissertation, we will generalize the work done by Almatrafi and Elsayed to a general order. We will do this by performing a complete Lie analysis for the following system of (k+ 2) th order difference equations un-1vn-k-1vn-k+1(An+Bnun-1vn-k-1),vn+1=un-k-1vn-1un-k+1(Cn+Dnun-k-1vn-1), (1) where An, Bn, Cn and Dn are real sequences. We will find the symmetries of (1) in terms of k. We will use these symmetries to find exact formulas for the solutions in terms of k. These exact formulas will be used to show that the results by Almatrafi and Elsayed are special cases of our findings.