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 Bäcklund--Darboux transformations for the lattice equations of Bogoyavlensky type.

20 pages, 2 figures

References in corpus (4)

• Generalized symmetry classification of discrete equations of a class depending on twelve parameters
• Method for searching higher symmetries for quad graph equations
• Cosymmetries and Nijenhuis recursion operators for difference equations
• Differential-difference equations associated with the fractional Lax operators

Cited by in corpus (11)

• Classification of five-point differential-difference equations
• Classification of five-point differential-difference equations II
• Integrable Möbius invariant evolutionary lattices of second order
• Perturbative Symmetry Approach for Differential-Difference Equations
• Non-invertible transformations for the classification of differential-difference equations
• Darboux transformations with tetrahedral reduction group and related integrable systems
• Integrable 7-point discrete equations and evolution lattice equations of order 2
• 3D-consistency of negative flows
• On consistent systems of difference equations
• Simplifications of Lax pairs for differential-difference equations by gauge transformations and (doubly) modified integrable equations
• Matrix Lax pairs under the gauge equivalence relation induced by the gauge group action and Miura-type transformations for lattice equations