title: |
Continuous and Discontinuous Piecewise Linear Solutions of the Linearly Forced Inviscid Burgers Equation |
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publication: |
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| volume-issue: | 15 - supplement 3 | |
| pages: | 264 - 276 | |
ISSN: |
1402-9251 | |
DOI: |
doi:10.2991/jnmp.2008.15.s3.26 (how to use a DOI) | |
author(s): |
Hans Lundmark, Jacek Szmigielski |
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publication date: |
October 2008 |
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abstract: |
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. |
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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |