On some integrable systems related to the Toda lattice

We discuss some of the integrable lattices introduced recently by R Yamilov. We demonstrate that they are closely related to the usual Toda lattice by means of a sort of Backlund transformations. We also apply the general procedure of integrable discretization and obtain their integrable finite-difference approximations. These novel integrable discrete-time systems are also related to the discrete-time Toda lattice by means of the Backlund transformations. The whole construction exploits the tri-Hamiltonian structure of the Toda lattice.