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

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Vakhnenko, Vyacheslav O. and Parkes, John; (2003) The connection of the Degasperis-Procesi equation with the Vakhnenko equation. In: Proceedings, 5th International Conference on Symmetry in Nonlinear Mathematical Physics (SYMMETRY 03). Proceedings of Institute of Mathematics of NAS of Ukraine, 50 . Institute of Mathematics of NAS, UKR, pp. 493-497. ISBN 9660232241

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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 periodic wave solutions are found; hump-like, loop-like and peak on 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 phase shift that depend on the ratio of wave amplitudes. In particular, there is a case when two interacted waves have phase shifts in the positive direction.

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