Picture of wind turbine against blue sky

Open Access research with a real impact...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs.

The Energy Systems Research Unit (ESRU) within Strathclyde's Department of Mechanical and Aerospace Engineering is producing Open Access research that can help society deploy and optimise renewable energy systems, such as wind turbine technology.

Explore wind turbine research in Strathprints

Explore all of Strathclyde's Open Access research content

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.