Formation and dynamics of shock waves in the Degasperis-Procesi equation
2007 (English)In: Journal of nonlinear science, ISSN 0938-8974, Vol. 17, no 3, 169-198 p.Article in journal (Refereed) Published
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.
IdentifiersURN: urn:nbn:se:liu:diva-39443DOI: 10.1007/s00332-006-0803-3Local ID: 48399OAI: oai:DiVA.org:liu-39443DiVA: diva2:260292