Towards the classification of integrable differential-difference equations in 2 + 1 dimensions

Abstract

We address the problem of classification of integrable differential-difference equations in 2+1 dimensions with one/two discrete variables. Our approach is based on the method of hydrodynamic reductions and its generalisation to dispersive equations. We obtain a number of classification results of scalar integrable equations including that of the intermediate long wave and Toda type.

16 pages

References in corpus (4)

• Characteristic Lie rings, finitely-generated modules and integrability conditions for 2+1 dimensional lattices
• Classification of 3-dimensional integrable scalar discrete equations
• On a (2+1)-dimensional generalization of the Ablowitz-Ladik lattice and a discrete Davey-Stewartson system
• Integrable equations and classical S-matrix

Cited by in corpus (3)

• Wave fronts and cascades of soliton interactions in the periodic two dimensional Volterra system
• Representations of sl(2,C) in the BGG category O and master symmetries
• Integrable systems of the intermediate long wave type in 2+1 dimensions