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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

   

 

Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - an analytic approach


Authors: Fritz Gesztesy and Rudi Weikard
Journal: Bull. Amer. Math. Soc. 35 (1998), 271-317
MSC (1991): Primary 34L40, 35Q53, 35Q55; Secondary 34B30, 34L05, 35Q51
MathSciNet review: 1638298
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Abstract: 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.


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Additional Information

Fritz Gesztesy
Affiliation: Department of Mathematics, University of Missouri, Columbia, MO 65211
Email: fritz@math.missouri.edu

Rudi Weikard
Affiliation: Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294-1170
Email: rudi@math.uab.edu

DOI: http://dx.doi.org/10.1090/S0273-0979-98-00765-4
PII: S 0273-0979(98)00765-4
Received by editor(s): May 20, 1998
Received by editor(s) in revised form: August 10, 1998
Additional Notes: Research supported in part by the US National Science Foundation under Grant Nos. DMS-9401816 and DMS-9623121.
Article copyright: © Copyright 1998 by the authors