New classes of hyperbolic-cotangent–type systems of difference equations solvable in closed form

Abstract

In the case of homogeneous linear difference equations with constant coefficients, only a relatively small part of the equations is practically solvable. This is connected to impossibility to solve all polynomial equations of degree bigger than four. In the case of nonlinear difference equations and systems the situation is even worse. So it is of interest to find new classes of practically solvable difference equations and systems. Recently, there have been presented several classes of practically solvable hyperbolic-cotangent–type systems of difference equations. Here, we present a new class of solvable systems of this type. It is a bit surprising that all the systems in the class are practically solvable, especially since several special cases are connected to some polynomials of degree eight.