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On positive type initial profiles for the KdV equation

Authors: Sergei Grudsky and Alexei Rybkin
Journal: Proc. Amer. Math. Soc. 142 (2014), 2079-2086
MSC (2010): Primary 34B20, 37K15, 47B35
Published electronically: March 10, 2014
MathSciNet review: 3182026
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Abstract: We show that the KdV flow evolves any real locally integrable initial profile $ q$ of the form $ q=r^{\prime }+r^{2}$, where $ r\in L_{\operatorname {loc}}^{2}$, $ r\vert _{\mathbb{R}_{+}}=0$ into a meromorphic function with no real poles.

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Additional Information

Sergei Grudsky
Affiliation: Departamento de Matematicas, CINVESTAV del I.P.N. Aportado Postal 14-740, 07000 Mexico, D.F., Mexico

Alexei Rybkin
Affiliation: Department of Mathematics and Statistics, University of Alaska Fairbanks, P.O. Box 756660, Fairbanks, Alaska 99775

Keywords: KdV equation, Titchmarsh-Weyl $m$-function, Hankel operators, Miura map
Received by editor(s): July 10, 2012
Published electronically: March 10, 2014
Additional Notes: The first author was partially supported by PROMEP (México) via “Proyecto de Redes” and by CONACYT grant 102800
The second author was supported in part by the NSF under grant DMS 1009673
Communicated by: James E. Colliander
Article copyright: © Copyright 2014 American Mathematical Society

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