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The Ablowitz-Ladik Hierarchy Revisited

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.

preprint2007arXivOpen access
Fritz GesztesyHelge HoldenJohanna MichorGerald Teschl
math-phmath.MPnlin.SI
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Open access4 authors3 topics
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Fritz GesztesyHelge HoldenJohanna MichorGerald Teschl

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