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) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided)

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:	Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User:	Andrew N W Hone
Date Deposited:	20 Nov 2018 10:53 UTC
Last Modified:	30 May 2019 08:20 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/70202 (The current URI for this page, for reference purposes)
Hone, Andrew N.W.:	https://orcid.org/0000-0001-9780-7369