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On the structure of the Bäcklund transformations for the relativistic lattices. (English) Zbl 1119.37330
Summary: 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.

MSC:
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
37K60 Lattice dynamics; integrable lattice equations
35A30 Geometric theory, characteristics, transformations in context of PDEs
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