The Ablowitz-Ladik Hierarchy Revisited
Exactly Solvable and Integrable Systems
2015-09-29 v3 Mathematical Physics
math.MP
Abstract
We provide a detailed recursive construction of the Ablowitz-Ladik (AL) hierarchy and its zero-curvature formalism. The two-coefficient AL hierarchy under investigation can be considered a complexified version of the discrete nonlinear Schr\"odinger equation and its hierarchy of nonlinear evolution equations. Specifically, we discuss in detail the stationary Ablowitz-Ladik formalism in connection with the underlying hyperelliptic curve and the stationary Baker-Akhiezer function and separately the corresponding time-dependent Ablowitz-Ladik formalism.
Keywords
Cite
@article{arxiv.nlin/0702058,
title = {The Ablowitz-Ladik Hierarchy Revisited},
author = {Fritz Gesztesy and Helge Holden and Johanna Michor and Gerald Teschl},
journal= {arXiv preprint arXiv:nlin/0702058},
year = {2015}
}
Comments
46 pages