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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2011
1. Verfasser: Mokhov, O.I.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2011
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/147398
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-147398
record_format dspace
spelling Mokhov, O.I.
2019-02-14T17:29:53Z
2019-02-14T17:29:53Z
2011
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
https://nasplib.isofts.kiev.ua/handle/123456789/147398
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.
This paper is a contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)” (June 14–18, 2010, Varna, Bulgaria). The full collection is available at http://www.emis.de/journals/SIGMA/SIDE-9.html. The work was carried out under partial financial support from the Russian Foundation for Basic Research (project no. 09-01-00762) and from the programme “Leading Scientific Schools” (project no. NSh-5413.2010.1).
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants
spellingShingle On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants
Mokhov, O.I.
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
author Mokhov, O.I.
author_facet Mokhov, O.I.
publishDate 2011
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/147398
citation_txt 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.
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