Legendre transformations on the triangular lattice

Abstract

The main purpose of the paper is to demonstrate that condition of invariance with respect to the Legendre transformations allows effectively isolate the class of integrable difference equations on the triangular lattice, which can be considered as discrete analogues of relativistic Toda type lattices. Some of obtained equations are new, up to the author knowledge. As an example, one of them is studied in more details, in particular, its higher continuous symmetries and zero curvature representation are found.

13 pages, latex

References in corpus (3)

• New integrable systems related to the relativistic Toda lattice
• A discrete time relativistic Toda lattice
• A collection of integrable systems of the Toda type in continuous and discrete time, with 2x2 Lax representations

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