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Dynamics of conservative peakons in a system of Popowicz

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)

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
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)

University of Kent Author Information

Barnes, Lucy.

Creator's ORCID:
CReDIT Contributor Roles:

Hone, Andrew N.W..

Creator's ORCID: https://orcid.org/0000-0001-9780-7369
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