English

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

R2 v1 2026-07-22T18:16:44.609Z