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

Symmetry Integrability and Geometry-Methods and Applications

article

Oleg I. Mokhov¹ 

[1] Centre for Nonlinear Studies, L.D.Landau Institute for Theoretical Physics, Russian Academy of Sciences;Department of Geometry and Topology, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University

关键词: consistency principle;    square and cubic lattices;    integrable discrete equation;    initial data;    determinant;    bent elementary square;    consistency “around a cube”;   

DOI  :  10.3842/SIGMA.2011.075

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown