Nonlinearization of the Lax pairs for discrete Ablowitz-Ladik hierarchy

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Original languageEnglish
Pages (from-to)829-853
Journal / PublicationJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 15 Mar 2007


The discrete Ablowitz-Ladik hierarchy with four potentials and the Hamiltonian structures are derived. Under a constraint between the potentials and eigenfunctions, the nonlinearization of the Lax pairs associated with the discrete Ablowitz-Ladik hierarchy 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. Each member in the discrete Ablowitz-Ladik hierarchy is decomposed into a Hamiltonian system of ordinary differential equations plus the discrete flow generated by the symplectic map. © 2006 Elsevier Inc. All rights reserved.

Research Area(s)

  • Discrete Ablowitz-Ladik hierarchy, Nonlinearization of the Lax pairs