A Difference Hamiltonian Operator and a Hierarchy of Generalized Toda Lattice Equations

A difference Hamiltonian operator with three arbitrary constants is presented. When the arbitrary constantsin the Hamiltonian operator are suitably chosen, a pair of Hamiltonian operators are given. The resulting Hamiltonianpair yields a difference hereditary operator. Using Mangri scheme of bi-Hamiltonian formulation, a hierarchy of thegeneralized Toda lattice equations is constructed. Finally,the discrete zero curvature representation is given for theresulting hierarchy.