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.
Highlights
It has been 300 years since the area of difference equations/recurrent relations started to attract a serious interest of scientist working in various branches of science
Among other things, we will demonstrate it on a concrete example of a nonlinear difference equation
Usefulness of the equation in solving many classes of nonlinear difference equations and systems has been recently demonstrated in many papers [32, 36,37,38,39,40,41,42]
Summary
It has been 300 years since the area of difference equations/recurrent relations started to attract a serious interest of scientist working in various branches of science. Usefulness of the equation in solving many classes of nonlinear difference equations and systems has been recently demonstrated in many papers [32, 36,37,38,39,40,41,42] (see the references therein; see [43, 44] and compare the methods therein with the solvability ones).
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