Geodesic
Legendre Transforms on a Triangular Lattice
Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 1, pp. 1-11

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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. 
@article{FAA_2000_34_1_a0,
     author = {V. E. Adler},
     title = {Legendre {Transforms} on a {Triangular} {Lattice}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2000_34_1_a0/}
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V. E. Adler. Legendre Transforms on a Triangular Lattice. Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 1, pp. 1-11. http://geodesic.mathdoc.fr/item/FAA_2000_34_1_a0/