On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2011
• Main Author: Mokhov, O.I.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2011
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147398
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants / O.I. Mokhov// Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 14 назв. — англ.

The paper is devoted to complete proofs of theorems on consistency on cubic lattices for 3×3 determinants. The discrete nonlinear equations on Z² defined by the condition that the determinants of all 3×3 matrices of values of the scalar field at the points of the lattice Z² 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 Z² defined by 3×3 determinants are proved.