Abstract
Gauss decomposition of the Lie algebra has been used to derive the Miura map for discrete completely integrable systems, which exactly reproduces the results obtained in a recent paper by Yang and Schmid. We have dealt with the cases of discrete mKdV, discrete sine - Gordon, discrete KdV and the Volterra system. Our approach has the advantage of yielding the Lax pair for the modified equation. It can also lead to a second stage of modified equation if the same procedure is repeated twice.
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