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Download fileOn the classification of discrete Hirota-type equations in 3D
journal contribution
posted on 2016-02-05, 11:02 authored by Evgeny FerapontovEvgeny Ferapontov, Vladimir NovikovVladimir Novikov, Ilia RoustemoglouIn the series of recent publications [15, 16, 18, 21] we have proposed a novel approach to the classification of integrable differential/difference equations in 3D based on the requirement that hydrodynamic reductions of the corresponding dispersionless limits are `inherited'
by the dispersive equations. In this paper we extend this to the fully discrete case. Based on the method of deformations of hydrodynamic reductions, we classify 3D discrete integrable Hirota-type equations within various particularly interesting subclasses. Our method can be viewed as an alternative to the conventional multi-dimensional consistency approach.
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