Legendre transforms on a triangular lattice
We show that the condition of invariance with respect to generalized Legendre transforms effectively singles out a class of integrable difference equations on a triangular lattice; these equations are discrete analogs of relativistic Toda lattices. Some of these equations are apparently new. For one of them, higher symmetries are written out and the zero curvature representation is obtained.
KeywordsHigh Symmetry Triangular Lattice Discrete Analog Toda Lattice Curvature Representation
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- 7.Yu. B. Suris, “A collection of integrable systems of the Toda type in continuous and discrete time, with 2×2 Lax representations,” Solv-int 9703004.Google Scholar