On the structure of the Bäcklund transformations for the relativistic lattices

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.

References in corpus (2)

• New integrable systems related to the relativistic Toda lattice
• A discrete time relativistic Toda lattice

Cited by in corpus (5)

• The Generalized Symmetry Method for Discrete Equations
• Reduction groups and related integrable difference systems of NLS type
• Multi-Component Extension of CAC Systems
• Integrable 7-point discrete equations and evolution lattice equations of order 2
• Solitons of a simple nonlinear model on the cubic lattice