Picture of two heads

Open Access research that challenges the mind...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including those from the School of Psychological Sciences & Health - but also papers by researchers based within the Faculties of Science, Engineering, Humanities & Social Sciences, and from the Strathclyde Business School.

Discover more...

The Connection of the Degasperis-Procesi equation with the Vakhnenko equation

Vakhnenko, V.O. and Parkes, J. (2004) The Connection of the Degasperis-Procesi equation with the Vakhnenko equation. In: Proceedings of Institute of Mathematics of NAS of Ukraine. Institute of Mathematics of NAS, pp. 493-497. ISBN 966-02-3224-1

[img]
Preview
PDF (strathprints002210.pdf)
strathprints002210.pdf

Download (237kB) | Preview

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.