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1 October 2018 Almost periodicity in time of solutions of the KdV equation
Ilia Binder, David Damanik, Michael Goldstein, Milivoje Lukic
Duke Math. J. 167(14): 2633-2678 (1 October 2018). DOI: 10.1215/00127094-2018-0015

Abstract

We study the Cauchy problem for the KdV equation tu6uxu+x3u=0 with almost periodic initial data u(x,0)=V(x). We consider initial data V, for which the associated Schrödinger operator is absolutely continuous and has a spectrum that is not too thin in a sense we specify, and we show the existence, uniqueness, and almost periodicity in time of solutions. This establishes a conjecture of Deift for this class of initial data. The result is shown to apply to all small analytic quasiperiodic initial data with Diophantine frequency vector.

Citation

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Ilia Binder. David Damanik. Michael Goldstein. Milivoje Lukic. "Almost periodicity in time of solutions of the KdV equation." Duke Math. J. 167 (14) 2633 - 2678, 1 October 2018. https://doi.org/10.1215/00127094-2018-0015

Information

Received: 23 March 2017; Revised: 1 January 2018; Published: 1 October 2018
First available in Project Euclid: 28 September 2018

zbMATH: 06872698
MathSciNet: MR3859361
Digital Object Identifier: 10.1215/00127094-2018-0015

Subjects:
Primary: 35Q53
Secondary: 34L40, 35B15, 37K10, 37K15

Rights: Copyright © 2018 Duke University Press

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Vol.167 • No. 14 • 1 October 2018
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