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

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

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...

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Main Author: Mokhov, O.I.
Format: Article
Language:English
Published: Інститут математики НАН України 2011
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/147398
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spelling irk-123456789-1473982019-02-15T01:25:15Z On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants Mokhov, O.I. 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. 2011 Article 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. 1815-0659 2010 Mathematics Subject Classification: 39A05; 52C07; 15A15; 37K10; 11H06 DOI:10.3842/SIGMA.2011.075 http://dspace.nbuv.gov.ua/handle/123456789/147398 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description 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.
format Article
author Mokhov, O.I.
spellingShingle Mokhov, O.I.
On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Mokhov, O.I.
author_sort Mokhov, O.I.
title On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants
title_short On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants
title_full On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants
title_fullStr On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants
title_full_unstemmed On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants
title_sort on initial data in the problem of consistency on cubic lattices for 3×3 determinants
publisher Інститут математики НАН України
publishDate 2011
url http://dspace.nbuv.gov.ua/handle/123456789/147398
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT mokhovoi oninitialdataintheproblemofconsistencyoncubiclatticesfor33determinants
first_indexed 2023-05-20T17:27:20Z
last_indexed 2023-05-20T17:27:20Z
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