On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants
Oleg Ivanovich Mokhov · Symmetry Integrability and Geometry Methods and Applications · 2011
The paper is devoted to complete proofs of theorems on consistency on cubic lattices for 3 × 3 determinants.The discrete nonlinear equations on Z 2 defined by the condition that the determinants of all 3×3 matrices of values of the scalar field at the points of the lattice Z 2 that form elementary 3 × 3 squares vanish are considered; some explicit concrete conditions of general position on initial data are formulated; and for arbitrary initial data satisfying these concrete conditions of general position, theorems on consistency on cubic lattices (a consistency "around a cube") for the considered discrete nonlinear equations on Z 2 defined by 3 × 3 determinants are proved.