A new class of solvable nonlinear difference equation systems

Abstract

The paper deals with the following system of nonlinear difference equations \begin{equation*} x_{n+1}=ax_{n}^{2}y_{n}+bx_{n}y_{n}^{2},\ y_{n+1}=cx_{n}^{2}y_{n}+dx_{n}y_{n}^{2},\ n\in \mathbb{N}_{0}, \end{equation*} where the initial values $x_0,y_0$ and the parameters $a$, $b$, $c$, $d$ are arbitrary real numbers, which is a new class of solvable systems of nonlinear difference equations. The general solution of the system is here obtained in closed form via a practical method.