A BILINEAR APPROACH TO DISCRETE MIURA-TRANSFORMATIONS

We present a systematic approach to the construction of Miura transfor mations for discrete Painleve equations. Our method is based on the bi linear formalism and we start with the expression of the nonlinear dis crete equation in terms of tau-functions. Elimination of tau-functions from the resulting system leads to another nonlinear equation, which is a ''modified'' version of the original equation. The procedure ther efore yields Miura transformations. In this letter, we illustrate this approach by reproducing previously known Miura transformations and co nstructing new ones. (C) 1998 Elsevier Science B.V.