Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1897463 | Physica D: Nonlinear Phenomena | 2006 | 17 Pages |
Abstract
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=KJâ1. 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Nicholas M. Ercolani, Guadalupe I. Lozano,