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

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 as proposed in [10,11]. We obtain a number of classification results of scalar integrable equations including that of the intermediate long wave and Toda type