Abstract
Travelling-wave solutions of the Degasperis-Procesi equation (DPE) are investigated. The
solutions are characterized by two parameters. Hump-like, loop-like and coshoidal periodicwave
solutions are found; hump-like, loop-like and peakon solitary-wave solutions are obtained
as well. Hone and Wang showed a connection between the DPE and the Vakhnenko
equation (VE). Comparing the solutions of the DPE and the VE, we observe that, for both
equations at interaction of waves, there are three kinds of phaseshift that depend on the
ratio of wave amplitudes. In particular, there is a case when two interacted waves have
phaseshifts in the positive direction.
| Original language | English |
|---|---|
| Title of host publication | Proceedings, 5th International Conference on Symmetry in Nonlinear Mathematical Physics (SYMMETRY 03) |
| Pages | 493-497 |
| Number of pages | 4 |
| Volume | 50 |
| Publication status | Published - 2004 |
| Event | 5th International Conference on Symmetry in Nonlinear Mathematical Physics - Kiev, Ukraine Duration: 23 Jun 2003 → 29 Jun 2003 |
Publication series
| Name | Proceedings of Institute of Mathematics of NAS of Ukraine |
|---|---|
| Publisher | Institute of Mathematics of NAS of Ukraine |
| Number | 1 |
| Volume | 50 |
Conference
| Conference | 5th International Conference on Symmetry in Nonlinear Mathematical Physics |
|---|---|
| Abbreviated title | Symmetry 03 |
| Country | Ukraine |
| City | Kiev |
| Period | 23/06/03 → 29/06/03 |
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Keywords
- Degasperis-Procesi equation
- coshoidal periodicwavesolutions
- Vakhnenko equation
Cite this
Vakhnenko, V. O., & Parkes, J. (2004). The connection of the Degasperis-Procesi equation with the Vakhnenko equation. In Proceedings, 5th International Conference on Symmetry in Nonlinear Mathematical Physics (SYMMETRY 03) (Vol. 50, pp. 493-497). (Proceedings of Institute of Mathematics of NAS of Ukraine; Vol. 50, No. 1).