  An explicit characterization of all elliptic algebro-geometric solutions of
the AKNS hierarchy is presented. Our approach is based on (an extension of) a
classical theorem of Picard, which guarantees the existence of solutions which
are elliptic of the second kind for n-th order ordinary differential equations
with elliptic coefficients associated with a common period lattice. As
by-products we offer a detailed Floquet analysis of Dirac-type differential
expressions with periodic coefficients, specifically emphasizing
algebro-geometric coefficients, and a constructive reduction of singular
hyperelliptic curves and their Baker-Akhiezer functions to the nonsingular
case.
