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A Bi-Hamiltonian Structure for the Integrable, Discrete Non-Linear Schrodinger System
- Publication Year :
- 2005
-
Abstract
- This paper shows that the Ablowitz-Ladik hierarchy of equations (a well-known integrable discretization of the Non-linear Schrodinger system) 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 (obtained by composing K and the inverse of J.) 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.<br />33 pages
- Subjects :
- Pure mathematics
Integrable system
Dynamical Systems (math.DS)
Poisson distribution
01 natural sciences
symbols.namesake
0103 physical sciences
FOS: Mathematics
0101 mathematics
Mathematics - Dynamical Systems
010306 general physics
Mathematics
Resolvent
010102 general mathematics
Mathematical analysis
Skew
Statistical and Nonlinear Physics
16. Peace & justice
Condensed Matter Physics
Nonlinear system
Mathematics - Symplectic Geometry
37K10, 37K60, 37K25, 53D17
Inverse scattering problem
symbols
Symplectic Geometry (math.SG)
Hamiltonian (quantum mechanics)
Schrödinger's cat
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....25363e66d3961859aff1cf0b32b42a4f