Article
in Methods of Spectral Analysis in Mathematical Physics, J. Janas (ed.) et al., 139-190, Oper. Theory Adv. Appl. 186, Birkhäuser, Basel, 2009 [DOI: 10.1007/978-3-7643-8755-6_8]

The Ablowitz-Ladik Hierarchy Revisited

Fritz Gesztesy, Helge Holden, Johanna Michor, and Gerald Teschl

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 Schrödinger 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.

MSC2000: Primary 37K15, 37K10; Secondary 39A12, 35Q55
Keywords: Ablowitz-Ladik hierarchy, discrete NLS

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