Elliptic Algebro-Geometric Solutions of the KdV and AKNS Hierarchies -   An Analytic Approach
  We provide an overview of elliptic algebro-geometric solutions of the KdV and AKNS hierarchies, with special emphasis on Floquet theoretic and spectral theoretic methods. Our treatment includes an effective characterization of all stationary elliptic KdV and AKNS solutions based on a theory developed by Hermite and Picard. 
Fritz Gesztesy and Rudi Weikard