Title	Instability of $H^1$-stable peakons in the Camassa-Holm and Novikov equations
Creator	Pelinovski, Dmitry
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
Type	Moving Image
File Format	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/
Aggregated Source Repository	DSpace

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