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Consistency on cubic lattices for determinants of arbitrary orders

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Abstract

We consider a special class of two-dimensional discrete equations defined by relations on elementary N × N squares, N > 2, of the square lattice ℤ2, and propose a new type of consistency conditions on cubic lattices for such discrete equations that is connected to bending elementary N × N squares, N > 2, in the cubic lattice ℤ3. For an arbitrary N we prove such consistency on cubic lattices for two-dimensional discrete equations defined by the condition that the determinants of values of the field at the points of the square lattice ℤ2 that are contained in elementary N × N squares vanish.

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Authors and Affiliations

  1. Centre for Nonlinear Studies, L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 119334, Russia

    O. I. Mokhov

  2. Department of Geometry and Topology, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    O. I. Mokhov

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  1. O. I. Mokhov
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Correspondence to O. I. Mokhov.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Vol. 266, pp. 202–217.

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Mokhov, O.I. Consistency on cubic lattices for determinants of arbitrary orders. Proc. Steklov Inst. Math. 266, 195–209 (2009). https://doi.org/10.1134/S0081543809030110

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  • DOI: https://doi.org/10.1134/S0081543809030110

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