On the structure of the Bäcklund transformations for the relativistic lattices
Vsevolod E. Adler
Abstract
The Bäcklund transformations for the relativistic lattices of the Toda type and their discrete analogues can be obtained as the composition of two duality transformations. The condition of invariance under this composition allows to distinguish effectively the integrable cases. Iterations of the Bäcklund transformations can be described in the terms of nonrelativistic lattices of the Toda type. Several multifield generalizations are presented.
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