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Nonlinear stability of stationary periodic solutions of the focusing NLS equation Deconinck, Bernard
Description
The spectral instabilities of the stationary periodic solutions of the focusing NLS equation were completely characterized recently. The crux of this characterization was the analysis of the non-self adjoint Lax pair for the focusing NLS equation. Although all solutions are unstable in the class of bounded perturbations, different solutions were found to be spectrally stable with respect to certain classes of periodic perturbations, with period an integer multiple of the solution period. We prove that all solutions that are spectrally stable are also (nonlinearly) orbitally stable, using dierent Krein signature calculations. Similar, more recent results for the sine-Gordon equation will be shown as well.
Item Metadata
Title |
Nonlinear stability of stationary periodic solutions of the focusing NLS equation
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-06-19T16:29
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Description |
The spectral instabilities of the stationary periodic solutions of the focusing NLS equation were completely characterized recently. The crux of this characterization was the analysis of the non-self adjoint Lax pair for the focusing NLS equation. Although all solutions are unstable in the class of bounded perturbations, different solutions were found to be spectrally stable with respect to certain classes of periodic perturbations, with period an integer multiple of the solution period. We prove that all solutions that are spectrally stable are also (nonlinearly) orbitally stable, using dierent Krein signature calculations. Similar, more recent results for the sine-Gordon equation will be shown as well.
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Extent |
31 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Washington
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Series | |
Date Available |
2017-12-17
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0362061
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International