KDV HIERARCHY VIA ABELIAN COVERINGS AND OPERATOR IDENTITIES

B. Eichinger; T. Vandenboom; P. Yuditskii

doi:10.1090/btran/30

KDV HIERARCHY VIA ABELIAN COVERINGS AND OPERATOR IDENTITIES

B. Eichinger, T. Vandenboom, P. Yuditskii

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We establish precise spectral criteria for potential functions V of reflectionless Schrödinger operators L_V = −∂x² + V to admit solutions to the Korteweg–de Vries (KdV) hierarchy with V as an initial value. More gener-ally, 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.

Original language	English
Pages (from-to)	1-44
Number of pages	44
Journal	Transactions of the American Mathematical Society Series B
Volume	6
DOIs	https://doi.org/10.1090/btran/30
State	Published - 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019 by the authors under.

Funding

Received by the editors March 13, 2018, and, in revised form, August 21, 2018. 2010 Mathematics Subject Classification. Primary 37K10, 37K15, 35Q53, 34L40. 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.

Funders	Funder number
National Science Foundation	P 29363-N32, DMS-1148609
Austrian Science Fund	4138-N32

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KDV HIERARCHY VIA ABELIAN COVERINGS AND OPERATOR IDENTITIES

Abstract

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Funding

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