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Periodic and solitary-wave solutions of the Degasperis-Procesi equation

Vakhnenko, V.O. and Parkes, E.J. (2004) Periodic and solitary-wave solutions of the Degasperis-Procesi equation. Chaos, Solitons and Fractals, 20 (5). pp. 1059-1073. ISSN 09600779

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Abstract

Travelling-wave solutions of the Degasperis-Procesi equation are investigated. The solutions are characterized by two parameters. For propagation in the positive x-direction, hump-like, inverted loop-like and coshoidal periodic-wave solutions are found; hump-like, inverted loop-like and peakon solitary-wave solutions are obtained as well. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. A transformed version of the Degasperis-Procesi equation, which is a generalization of the Vakhnenko equation, is also considered. For propagation in the positive x-direction, hump-like, loop-like, inverted loop-like, bell-like and coshoidal periodic-wave solutions are found; loop-like, inverted loop-like and kink-like solitary-wave solutions are obtained as well. For propagation in the negative x-direction, well-like and inverted coshoidal periodic-wave solutions are found; well-like and inverted peakon solitary-wave solutions are obtained as well. In an appropriate limit, the previously known solutions of the Vakhnenko equation are recovered.

Item type: Article
ID code: 2198
Keywords: Degasperis-Procesi equation, Vakhnenko equation, wave solutions, coshoidal wave, Mathematics, Physics
Subjects: Science > Mathematics
Science > Physics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
Depositing user: Strathprints Administrator
Date Deposited: 06 Jan 2007
Last modified: 12 Mar 2012 10:37
URI: http://strathprints.strath.ac.uk/id/eprint/2198

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