2013/12/05 by E. V. Ferapontov, Ferapontov, E. V., V. S. Novikov +3 · 1 citation
Physics and Astronomy · #35Q51 #37K10 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #msc:35Q51 #msc:37K10 #nlin.SI
paper · pdf · doi:10.48550/arxiv.1312.1574
29 pages
arxiv created 2013/12/05 · arxiv updated 2013/12/06
In the series of recent publications 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. Our only constraint is that the initial ansatz possesses a non-degenerate dispersionless limit (this is the case for all known Hirota-type equations). Based on the method of deformations of hydrodynamic reductions, we classify discrete 3D integrable Hirota-type equations within various particularly interesting subclasses. Our method can be viewed as an alternative to the conventional multi-dimensional consistency approach.