On the classification of discrete Hirota-type equations in 3D
journal contributionposted on 05.02.2016, 11:02 by Evgeny FerapontovEvgeny Ferapontov, Vladimir NovikovVladimir Novikov, Ilia Roustemoglou
In 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.
- Mathematical Sciences