# 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)

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.