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

Lundmark, Hans (author): Linköpings universitet,Tillämpad matematik,Tekniska högskolan

Szmigielski, Jacek (author)

(creator_code:org_t)

2008
2008
English.
In: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 15, s. 264-276

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Abstract Subject headings

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.

About the subject

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