Representations of solutions to linear and bilinear difference equations and systems of bilinear difference equations

Abstract

We represent general solution to a homogeneous linear difference equation of second order in terms of a specially chosen solution to the equation and apply it to get a representation of general solution to the bilinear difference equation in terms of a solution to an associate difference equation of second order, considerably generalizing some recent results in an elegant way. We also present the corresponding representations for some systems of bilinear difference equations. Many historical notes not so known to wide audience are also presented, and we offer an answer to an open question regarding the attribution of the bilinear difference equation.