Fritz Gesztesy, Helge Holden, Johanna Michor, and Gerald Teschl
The Ablowitz-Ladik Hierarchy Revisited
(155K, LaTeX2e)

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 
Schroedinger 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.