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Transactions of the American Mathematical Society Series B

ISSN 2330-0000

   
 
 

 

KdV hierarchy via Abelian coverings and operator identities


Authors: B. Eichinger, T. VandenBoom and P. Yuditskii
Journal: Trans. Amer. Math. Soc. Ser. B 6 (2019), 1-44
MSC (2010): Primary 37K10, 37K15, 35Q53, 34L40
DOI: https://doi.org/10.1090/btran/30
Published electronically: January 2, 2019
Previous version of record: Original version posted January 2, 2019
Current version of record: Current version corrects errors introduced by the publisher.
MathSciNet review: 3894927
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Abstract | References | Similar Articles | Additional Information

Abstract: We establish precise spectral criteria for potential functions $ V$ of reflectionless Schrödinger operators $ L_V = -\partial _x^2 + V$ to admit solutions to the Korteweg-de Vries (KdV) hierarchy with $ V$ as an initial value. More generally, our methods extend the classical study of algebro-geometric solutions for the KdV hierarchy to noncompact Riemann surfaces by defining generalized Abelian integrals and analogues of the Baker-Akhiezer function on infinitely connected domains with a uniformly thick boundary satisfying a fractional moment condition.


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Additional Information

B. Eichinger
Affiliation: Center for Mathematical Science, Lund University, 22100 Lund, Sweden

T. VandenBoom
Affiliation: Department of Mathematics, Rice University, Houston, Texas 77005-1892

P. Yuditskii
Affiliation: Institute for Analysis, Johannes Kepler University, A-4040 Linz, Austria

DOI: https://doi.org/10.1090/btran/30
Received by editor(s): March 13, 2018
Received by editor(s) in revised form: August 21, 2018
Published electronically: January 2, 2019
Additional Notes: The first author was supported by the Austrian Science Fund FWF, project no. J 4138-N32.
The second author was supported in part by NSF grant DMS-1148609.
The third author was supported by the Austrian Science Fund FWF, project no. P 29363-N32.
Article copyright: © Copyright 2019 by the author under Creative Commons Attribution 3.0 License (CC BY 3.0)