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Formation and dynamics of shock waves in the Degasperis-Procesi equation
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.ORCID iD: 0000-0003-4137-8272
2007 (English)In: Journal of nonlinear science, ISSN 0938-8974, Vol. 17, no 3, 169-198 p.Article in journal (Refereed) Published
Abstract [en]

Solutions of the Degasperis-Procesi nonlinear wave equation may develop discontinuities in finite time. As shown by Coclite and Karlsen, there is a uniquely determined entropy weak solution which provides a natural continuation of the solution past such a point. Here we study this phenomenon in detail for solutions involving interacting peakons and antipeakons. We show that a jump discontinuity forms when a peakon collides with an antipeakon, and that the entropy weak solution in this case is described by a "shockpeakon" ansatz reducing the PDE to a system of ODEs for positions, momenta, and shock strengths.

Place, publisher, year, edition, pages
2007. Vol. 17, no 3, 169-198 p.
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Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-39443DOI: 10.1007/s00332-006-0803-3Local ID: 48399OAI: oai:DiVA.org:liu-39443DiVA: diva2:260292
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-11-14

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Lundmark, Hans

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