Search: onr:"swepub:oai:DiVA.org:liu-139590" >
Dynamics of interla...
-
Lundmark, Hans,1970-Linköpings universitet,Matematik och tillämpad matematik,Tekniska fakulteten
(author)
Dynamics of interlacing peakons (and shockpeakons) in the Geng–Xue equation
- Article/chapterEnglish2017
Publisher, publication year, extent ...
-
2017-01-23
-
Oxford University Press,2017
-
electronicrdacarrier
Numbers
-
LIBRIS-ID:oai:DiVA.org:liu-139590
-
https://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-139590URI
-
https://doi.org/10.1093/integr/xyw014DOI
Supplementary language notes
-
Language:English
-
Summary in:English
Part of subdatabase
Classification
-
Subject category:ref swepub-contenttype
-
Subject category:art swepub-publicationtype
Notes
-
We consider multipeakon solutions, and to some extent also multishockpeakon solutions, of a coupled two- component integrable PDE found by Geng and Xue as a generalization of Novikov’s cubically nonlinear Camassa–Holm type equation. In order to make sense of such solutions, we find it necessary to assume that there are no overlaps, meaning that a peakon or shockpeakon in one component is not allowed to occupy the same position as a peakon or shockpeakon in the other component. Therefore one can distinguish many inequivalent configurations, depending on the order in which the peakons or shockpeakons in the two components appear relative to each other. Here we are particularly interested in the case of interlacing peakon solutions, where the peakons alternatingly occur in one component and in the other. Based on explicit expressions for these solutions in terms of elementary functions, we describe the general features of the dynamics, and in particular the asymptotic large-time behaviour (assuming that there are no antipeakons, so that the solutions are globally defined). As far as the positions are concerned, interlacing Geng–Xue peakons display the usual scattering phenomenon where the peakons asymptotically travel with constant velocities, which are all distinct, except that the two fastest peakons (the fastest one in each component) will have the same velocity. However, in contrast to many other peakon equations, the amplitudes of the peakons will not in general tend to constant values; instead they grow or decay exponentially. Thus the logarithms of the amplitudes (as functions of time) will asymptotically behave like straight lines, and comparing these lines for large positive and negative times, one observes phase shifts similar to those seen for the positions of the peakons (and also for the positions of solitons in many other contexts). In addition to these K+K interlacing pure peakon solutions, we also investigate 1+1 shockpeakon solutions, and collisions leading to shock formation in a 2+2 peakon–antipeakon solution.
Subject headings and genre
Added entries (persons, corporate bodies, meetings, titles ...)
-
Szmigielski, JacekDepartment of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada
(author)
-
Linköpings universitetMatematik och tillämpad matematik
(creator_code:org_t)
Related titles
-
In:Journal of Integrable Systems: Oxford University Press2:12058-5985
Internet link
Find in a library
To the university's database