A bi-Hamiltonian structure for the integrable, discrete non-linear Schrodinger system

PHYSICA D-NONLINEAR PHENOMENA

卷:218

Article

Ercolani, Nicholas M. ; Lozano, Guadalupe I.

关键词: discrete integrable equations;    lattice dynamics;    inverse scattering;    Poisson geometry;    bi-Hamiltonian structures;   

DOI  :  10.1016/j.physd.2006.04.014

来源: Elsevier

【 摘 要 】

This paper shows that the AL (Ablowitz-Ladik) hierarchy of (integrable) equations can be explicitly viewed as a hierarchy of commuting flows which: (a) are Hamiltonian with respect to both a standard, local Poisson operator J, and a new non-local, skew, almost Poisson operator K, on the appropriate space; (b) can be recursively generated from a recursion operator R = KJ(-1). In addition, the proof of these facts relies upon two new pivotal resolvent identities which suggest a general method for uncovering bi-Hamiltonian structures for other families of discrete, integrable equations. (c) 2006 Elsevier B.V. All rights reserved.

【 授权许可】

Free