in Methods of Spectral Analysis in Mathematical Physics, J. Janas (ed.) et al., 139-190,
  Oper. Theory Adv. Appl. 186, Birkhäuser, Basel, 2008.

The Ablowitz-Ladik hierarchy revisited

F. Gesztesy, H. Holden, J. Michor, and G. Teschl

Keywords: Ablowitz-Ladik hierarchy, discrete NLS.

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.

MSC: Primary 37K15, 37K10; Secondary 39A12, 35Q55.

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ESI Preprint 1897
arXiv:nlin/0702058v1

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