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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2011 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2011
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147398 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862713546447519744 |
|---|---|
| author | Mokhov, O.I. |
| author_facet | Mokhov, O.I. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-07T17:44:54Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147398 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:44:54Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants Mokhov, O.I. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147398 |
| work_keys_str_mv | AT mokhovoi oninitialdataintheproblemofconsistencyoncubiclatticesfor33determinants |