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The Ablowitz-Ladik Hierarchy Revisited

Fritz Gesztesy·Helge Holden·Johanna Michor·Gerald Teschl
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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 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.

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Fritz Gesztesy, Helge Holden, Johanna Michor, Gerald Teschl. 2007-12-15. The Ablowitz-Ladik Hierarchy Revisited. https://doi.org/10.1007/978-3-7643-8755-6_8

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