Bargmann Type Systems for the Generalization of Toda Lattices - Fang Li; Liping Lu (Journal of Applied Mathematics, 2014)
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.