On discrete integrable equations of higher order

Abstract

We study 2D 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 B\"acklund--Darboux transformations for the lattice equations of Bogoyavlensky type.Comment: 20 pages, 2 figure