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Journal of Applied Mathematics
Volume 2014, Article ID 287529, 8 pages
Research Article

Bargmann Type Systems for the Generalization of Toda Lattices

1College of Science, Henan University of Technology, 100 Lianhua Road, Zhengzhou, Henan 450001, China
2Department of Information Engineering, Henan College of Finance and Taxation, Zhengkai Road, Zhengzhou, Henan 451464, China

Received 5 April 2014; Accepted 24 May 2014; Published 9 June 2014

Academic Editor: Senlin Guo

Copyright © 2014 Fang Li and Liping Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.