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NONEXISTENCE OF SMALL, SMOOTH, TIME-PERIODIC, SPATIALLY PERIODIC SOLUTIONS FOR NONLINEAR SCHRODINGER EQUATIONS
Journal article   Open access   Peer reviewed

NONEXISTENCE OF SMALL, SMOOTH, TIME-PERIODIC, SPATIALLY PERIODIC SOLUTIONS FOR NONLINEAR SCHRODINGER EQUATIONS

David M. Ambrose and J. Douglas Wright
Quarterly of applied mathematics, v 77(3), pp 579-590
01 Sep 2019
url
https://doi.org/10.1090/qam/1519View
Accepted (AM)Open Access (Publisher-Specific) Open

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
We study the question of nonexistence of small spatially periodic, time-periodic solutions for cubic nonlinear Schrodinger equations. We prove that in certain regions of the period-amplitude plane, time-periodic solutions do not exist. To be more precise, we prove that for almost any value in a bounded set of possible temporal periods, there is an amplitude threshold, below which any initial value is not the initial value for a time-periodic solution. The proof requires a certain level of Sobolev regularity on solutions. The methods used are not based on any special structure of the nonlinear Schrodinger equation, and can be applied more generally.

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Web of Science research areas
Mathematics, Applied
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