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Zbl 0935.37037
Suris, Yuri B.
On some integrable systems related to the Toda lattice. (English)
[J] J. Phys. A, Math. Gen. 30, No.6, 2235-2249 (1997). ISSN 0305-4470

Integrable lattices introduced recently by R. Yamilov are shown to be closely related to the usual Toda lattice by means of a sort of Bäcklund transformations. These lattices correspond to three different parametrizations of the phase variables by means of canonically conjugated coordinates and momenta, resulting in three different invariant Poisson structures. The author applies the general procedure of integrable discretization and obtains their integrable finite-difference approximations. Explicit integrable discretizations of these lattices are considered and they are shown to be different tri-Hamiltonian discrete-time systems, whose natural phase space is that of the relativistic Toda lattice.
[Samir Musayev (Baku)]

MSC 2000:: *37K10 Completely integrable systems etc.
37K05 Hamiltonian structures, etc.
37N20 Dynamical systems in other branches of physics
70H05 Hamilton's equations
70F99 Dynamics of a system of particles
37K35 Lie-Bäcklund and other transformations

Keywords: lattice models; integrable systems; Hamiltonian equations; integrable lattices; Toda lattice; Bäcklund transformations; Poisson structures; tri-Hamiltonian

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Zentralblatt MATH Berlin [Germany]