The Ablowitz-Ladik Hierarchy Revisited

Details The Ablowitz-Ladik Hierarchy Revisited The Ablowitz-Ladik Hierarchy Revisited

2007-02-28

arxiv.org/abs/nlin/0702058v3

in Methods of Spectral Analysis in Mathematical Physics, J. Janas (ed.) et al., 139-190, Oper. Theory Adv. Appl. 186, Birkhaeu

Nonlinear Sciences

Exactly Solvable and Integrable Systems

46 pages

Scientific paper

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 Schr\"odinger 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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