Barnes, Lucy, Hone, Andrew N.W. (2019) Dynamics of conservative peakons in a system of Popowicz. Physics Letters A, 383 (5). pp. 406-413. ISSN 0375-9601. (doi:10.1016/j.physleta.2018.11.015) (KAR id:70202)
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Official URL: https://doi.org/10.1016/j.physleta.2018.11.015 |
Abstract
We consider a two-component Hamiltonian system of partial
differential equations with quadratic nonlinearities introduced by
Popowicz, which has the form of a coupling between the Camassa-Holm and Degasperis-Procesi equations.
Despite having reductions to these two integrable partial differential equations, the Popowicz
system itself is not integrable. Nevertheless, as one of the authors showed with Irle, it admits
distributional solutions of peaked soliton (peakon) type, with the dynamics of $N$
peakons being determined by a Hamiltonian system on a phase space of dimension $3N$.
As well as the trivial case of a single peakon ($N=1$), the case $N=2$ is Liouville
integrable. We present the explicit solution for the two-peakon dynamics, and describe
some of the novel features of the interaction of peakons in the Popowicz system.
Item Type: | Article |
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DOI/Identification number: | 10.1016/j.physleta.2018.11.015 |
Uncontrolled keywords: | Peakons; Popowicz system; Distributions; Hamiltonian dynamics |
Subjects: | Q Science > QA Mathematics (inc Computing science) |
Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | Andrew Hone |
Date Deposited: | 20 Nov 2018 10:53 UTC |
Last Modified: | 04 Mar 2024 19:54 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/70202 (The current URI for this page, for reference purposes) |
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