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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| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2011
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147398 |
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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 |
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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 |
2025-07-11T02:00:59Z |
| last_indexed |
2025-07-11T02:00:59Z |
| _version_ |
1837314091696259072 |