Volterra difference equations arise in the mathematical modeling of some real phenomena, and also in numerical schemes for solving differential and integral equations (cf. [7, 8] and the references therein). One of the basic methods in the theory of stability and boundedness of Volterra difference equations is the direct Lyapunov method (see [1, 3, 4] and the references therein). But finding th...

We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential difference equations in mathematical physics via the lattice equation and the dis...

Recently, there has been a lot of interest in studying the global attractivity, the boundedness character, and the periodicity nature of nonlinear difference equations see for example, [1– 22]. The study of the nonlinear rational difference equations of a higher order is quite challenging and rewarding, and the results about these equations offer prototypes towards the development of the basic ...