Article
Int. Math. Res. Not. 2007, Art. ID rnm082, 55 pp (2007) [DOI: 10.1093/imrn/rnm082]

Algebro-Geometric Finite-Band Solutions of the Ablowitz-Ladik Hierarchy

Fritz Gesztesy, Helge Holden, Johanna Michor, and Gerald Teschl

Abstract
We provide a detailed derivation of all complex-valued algebro-geometric finite-band solutions of the Ablowitz-Ladik hierarchy. In addition, we survey a recursive construction of the Ablowitz-Ladik hierarchy and its zero-curvature and Lax formalism.

MSC2000: Primary 37K15, 37K10; Secondary 39A12, 35Q55
Keywords: Ablowitz-Ladik hierarchy, discrete NLS, algebro-geometric solutions.

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