Algebro-Geometric Finite-Gap Solutions of the Ablowitz-Ladik Hierarchy
  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. 
Fritz Gesztesy, Helge Holden, Johanna Michor, and Gerald Teschl