On consistency of determinants on cubic lattices

TL;DR

This paper introduces a modified consistency condition for certain two-dimensional discrete equations on cubic lattices and proves that determinant-based nonlinear equations of order greater than two are consistent under this new criterion.

Contribution

It proposes a new consistency condition for discrete equations on cubic lattices and demonstrates that determinant-based equations of order N > 2 satisfy this condition.

Findings

Determinant-based nonlinear equations of order N > 2 are consistent on cubic lattices.

A modified consistency condition for two-dimensional discrete equations is proposed.

The paper establishes the consistency of specific classes of equations under the new criterion.

Abstract

We propose a modified condition of consistency on cubic lattices for some special classes of two-dimensional discrete equations and prove that the discrete nonlinear equations defined by determinants of matrices of orders N > 2 are consistent on cubic lattices in this sense.