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 |
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| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2011
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| 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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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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2025-12-07T17:44:54Z |
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2025-12-07T17:44:54Z |
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