Bargmann Type Systems for the Generalization of Toda Lattices

Fang Li and Liping Lu

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/287529

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:287529

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