A Characterization of All Elliptic Solutions of the AKNS Hierarchy

Details A Characterization of All Elliptic Solutions of the AKNS Hierarchy A Characterization of All Elliptic Solutions of the AKNS Hierarchy

1997-05-28

arxiv.org/abs/solv-int/9705018v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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Scientific paper

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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