On a system of second-order difference equations
Abstract
We obtain explicit formulas for the solutions of the system of second-order difference equations of the form xn+ 1 = xn yn-1yn (an + bn xn yn - 1), yn+1 = xn - 1 ynxn (cn+dn xn-1 yn), where (an)n∈ N0,\; (bn)n∈ N0, \;(cn)n∈ N0 and (dn)n∈ N0 are real sequences. We use Lie symmetry analysis to derive non-trivial symmetries and thereafter, exact solutions are obtained.
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