Journal of Nonlinear Mathematical Physics

Volume 15, Issue supplement 3, October 2008, Pages 264 - 276

Continuous and Discontinuous Piecewise Linear Solutions of the Linearly Forced Inviscid Burgers Equation

Authors
Hans Lundmark, Jacek Szmigielski
Corresponding Author
Hans Lundmark
Available Online 1 October 2008.
DOI
10.2991/jnmp.2008.15.s3.26How to use a DOI?
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.

Copyright
© 2008, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
15 - supplement 3
Pages
264 - 276
Publication Date
2008/10/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2008.15.s3.26How to use a DOI?
Copyright
© 2008, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Hans Lundmark
AU  - Jacek Szmigielski
PY  - 2008
DA  - 2008/10/01
TI  - Continuous and Discontinuous Piecewise Linear Solutions of the Linearly Forced Inviscid Burgers Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 264
EP  - 276
VL  - 15
IS  - supplement 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.s3.26
DO  - 10.2991/jnmp.2008.15.s3.26
ID  - Lundmark2008
ER  -