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International Journal of Computer Mathematics Volume 87, 2010 - Issue 10
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Section B

Solitary-wave solutions of the Degasperis–Procesi equation by means of the homotopy analysis method

S. Abbasbandy Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran; Department of Mathematics, Imam Khomeini International University, Ghazvin, 34149-16818, IranCorrespondence[email protected]
&
E. J. Parkes Department of Mathematics, University of Strathclyde, Glasgow, UK
Pages 2303-2313 | Received 24 Nov 2007, Accepted 04 Nov 2008, Published online: 20 May 2010
 
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Abstract

The homotopy analysis method (HAM) is applied to the Degasperis–Procesi equation in order to find analytic approximations to the known exact solitary-wave solutions for the solitary peakon wave and the family of solitary smooth-hump waves. It is demonstrated that the approximate solutions agree well with the exact solutions. This provides further evidence that the HAM is a powerful tool for finding excellent approximations to nonlinear solitary waves.

2000 AMS Subject Classifications :

Acknowledgements

The authors would like to thank the anonymous referees for their valuable suggestions.

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