07-50 Fritz Gesztesy, Helge Holden, Johanna Michor, and Gerald Teschl

The Ablowitz-Ladik Hierarchy Revisited (155K, LaTeX2e) Feb 28, 07

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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.

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