97-270 F. Gesztesy and R. Weikard

A Characterization of All Elliptic Solutions of the AKNS Hierarchy (120K, amslatex) May 14, 97

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Abstract. 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.

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