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Continuous and Discontinuous Piecewise Linear Solutions of the Linearly Forced Inviscid Burgers Equation
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0003-4137-8272
2008 (English)In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 15, 264-276 p.Article in journal (Refereed) Published
Abstract [en]

We study a class of piecewise linear solutions to the inviscid Burgers equation driven by a linear forcing term. Inspired by the analogy with peakons, we think of these solutions as being made up of solitons situated at the breakpoints. We derive and solve ODEs governing the soliton dynamics, first for continuous solutions, and then for more general shock wave solutions with discontinuities. We show that triple collisions of solitons cannot take place for continuous solutions, but give an example of a triple collision in the presence of a shock.

Place, publisher, year, edition, pages
2008. Vol. 15, 264-276 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-17147DOI: 10.2991/jnmp.2008.15.s3.26OAI: oai:DiVA.org:liu-17147DiVA: diva2:202137
Available from: 2009-03-07 Created: 2009-03-07 Last updated: 2017-12-13

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Lundmark, Hans

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