On the non-integrability of the Popowicz peakon system
| dc.creator | Hone, Andrew N. W. | |
| dc.creator | Irle, Michael V. | |
| dc.date | 2008-08-19 | |
| dc.date.accessioned | 2026-07-07T09:57:21Z | |
| dc.date.available | 2026-07-07T09:57:21Z | |
| dc.description | We consider a coupled system of Hamiltonian partial differential equations introduced by Popowicz, which has the appearance of a two-field coupling between the Camassa-Holm and Degasperis-Procesi equations. The latter equations are both known to be integrable, and admit peaked soliton (peakon) solutions with discontinuous derivatives at the peaks. A combination of a reciprocal transformation with Painlevé analysis provides strong evidence that the Popowicz system is non-integrable. Nevertheless, we are able to construct exact travelling wave solutions in terms of an elliptic integral, together with a degenerate travelling wave corresponding to a single peakon. We also describe the dynamics of N-peakon solutions, which is given in terms of an Hamiltonian system on a phase space of dimension 3N. | |
| dc.description | 8 pages, AIMS class file. Proceedings of AIMS conference on Dynamical Systems, Differential Equations and Applications, Arlington, Texas, 2008 | |
| dc.identifier | https://arxiv.org/abs/0808.2617 | |
| dc.identifier | http://arxiv.org/abs/0808.2617 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167312 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | Pattern Formation and Solitons | |
| dc.title | On the non-integrability of the Popowicz peakon system | |
| dc.type | text |