On discrete 2D integrable equations of higher order

We study two-dimensional discrete integrable equations of order 1 with respect to one independent variable and m with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The examples are related to the Bäcklund-Darboux transformations for the lattice equations of Bogoyavlensky type. © 2014 IOP Publishing Ltd.