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Bargmann Type Systems for the Generalization of Toda Lattices

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  • Fang Li
  • Liping Lu

Abstract

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.

Suggested Citation

  • Fang Li & Liping Lu, 2014. "Bargmann Type Systems for the Generalization of Toda Lattices," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, June.
    • Handle: RePEc:hin:jnljam:287529
    DOI: 10.1155/2014/287529
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