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New integrable systems related to the relativistic Toda lattice. (English) Zbl 1001.37508
Summary: The bi-Hamiltonian structure of the relativistic Toda lattice is exploited to introduce some new integrable lattice systems. Their integrable discretizations are obtained by means of the general procedure proposed recently by the author. Bäcklund transformations between the new systems and the relativistic Toda lattice (in both the continuous and discrete time formulations) are established.
MSC:
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
70F10n-body problems
70H05Hamilton’s equations