Consistency on cubic lattices for determinants of arbitrary orders

Details Consistency on cubic lattices for determinants of arbitrary orders Consistency on cubic lattices for determinants of arbitrary orders

2009-10-11

arxiv.org/abs/0910.2044v1

Proceedings of the Steklov Institute of Mathematics, 2009, Vol. 266, pp. 195-209

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

We consider a special class of two-dimensional discrete equations defined by relations on elementary NxN squares, N>2, of the square lattice Z^2, and propose a new type of consistency conditions on cubic lattices for such discrete equations that is connected to bending elementary NxN squares, N>2, in the cubic lattice Z^3. 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 Z^2 that are contained in elementary NxN squares vanish.

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