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Instability of $H^1$-stable peakons in the Camassa-Holm and Novikov equations Pelinovski, Dmitry
Description
It is well-known that peakons in the Camassa-Holm equation and other integrable generalizations of the KdV equation are $H^1$-orbitally stable thanks to the presence of conserved quantities and properties of peakons as constrained energy minimizers. By using the method of characteristics, we prove that piecewise $C^1$ perturbations to peakons grow in time in spite of their stability in the $H^1$-norm. We also show that the linearized stability analysis near peakons contradicts the $H^1$-orbital stability result for the Camassa-Holm equation, hence the passage from the linear to nonlinear theory is false.
Item Metadata
| Title |
Instability of $H^1$-stable peakons in the Camassa-Holm and Novikov equations
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2019-07-01T14:47
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| Description |
It is well-known that peakons in the Camassa-Holm equation and other integrable generalizations of the KdV equation are $H^1$-orbitally stable thanks to the presence of conserved quantities and properties of peakons as constrained energy minimizers. By using the method of characteristics, we prove that piecewise $C^1$ perturbations to peakons grow in time in spite of their stability in the $H^1$-norm. We also show that the linearized stability analysis near peakons contradicts the $H^1$-orbital stability result for the Camassa-Holm equation, hence the passage from the linear to nonlinear theory is false.
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| Extent |
36.0 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: McMaster University
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| Series | |
| Date Available |
2019-12-29
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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 |
10.14288/1.0387374
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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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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International