Bargmann type systems for the generalization of Toda lattices

Under a constraint between the potentials and eigenfunctions,the nonlinearization of the lax pairs associated with the discrete hierarchy of a generalization of the toda lattice equation is proposed,which leads to a new symplectic map and a class of finite-dimensional hamiltonian systems. the generating function of the integrals of motion is presented,by which the symplectic map and these finite-dimensional hamiltonian systems are further proved to be completely integrable in the liouville sense. finally,the representation of solutions for a lattice equation in the discrete hierarchy is obtained. © 2014 fang li and liping lu.