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On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants
Інший ID:
2010 Mathematics Subject Classification: 39A05; 52C07; 15A15; 37K10; 11H06
DOI:10.3842/SIGMA.2011.075
DOI:10.3842/SIGMA.2011.075
Посилання:
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.
Підтримка:
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).
Дата:
2011
Переглядів:
443
Завантажень:
231
Анотація:
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.
