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Title	Instability of $H^1$-stable peakons in the Camassa-Holm and Novikov equations
Creator	Dmitry Pelinovski
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2019-07-01T14:47
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.
Extent	36.0 minutes
Subject	Mathematics Partial Differential Equations, Fourier Analysis
Geographic Location	Banff (Alta.)
Type	Moving Image
FileFormat	video/mp4
Language	eng
Notes	Author affiliation: McMaster University
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2019-12-29
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0387374
URI	http://hdl.handle.net/2429/73013
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
AggregatedSourceRepository	DSpace

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