A Bilinear Approach to Discrete Miura Transformations

Details A Bilinear Approach to Discrete Miura Transformations A Bilinear Approach to Discrete Miura Transformations

1998-09-24

arxiv.org/abs/solv-int/9809014v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

7 pages in TeX, to appear in Phys. Letts. A

Scientific paper

10.1016/S0375-9601(98)00624-0

We present a systematic approach to the construction of Miura transformations for discrete Painlev\'e equations. Our method is based on the bilinear formalism and we start with the expression of the nonlinear discrete 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 therefore yields Miura transformations. In this letter, we illustrate this approach by reproducing previously known Miura transformations and constructing new ones.

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