Journal article
NONEXISTENCE OF SMALL, SMOOTH, TIME-PERIODIC, SPATIALLY PERIODIC SOLUTIONS FOR NONLINEAR SCHRODINGER EQUATIONS
Quarterly of applied mathematics, v 77(3), pp 579-590
01 Sep 2019
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
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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Details
- Title
- NONEXISTENCE OF SMALL, SMOOTH, TIME-PERIODIC, SPATIALLY PERIODIC SOLUTIONS FOR NONLINEAR SCHRODINGER EQUATIONS
- Creators
- David M. Ambrose - Drexel UniversityJ. Douglas Wright - Drexel Univ, Dept Math, Philadelphia, PA 19104 USA
- Publication Details
- Quarterly of applied mathematics, v 77(3), pp 579-590
- Publisher
- Brown Univ
- Number of pages
- 12
- Grant note
- DMS-1515849; DMS-1511488 / National Science Foundation; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000469390700007
- Scopus ID
- 2-s2.0-85073758771
- Other Identifier
- 991019168998704721
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- Web of Science research areas
- Mathematics, Applied