The travelling wave solutions for non-linear initial-value problems using the homotopy perturbation method

Authors: Zayed, E. M. E.¹; Nofal, T. A.²; Gepreel, K. A.¹

Source: Applicable Analysis, Volume 88, Number 4, April 2009 , pp. 617-634(18)

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Abstract:

In this article, we have used the homotopy perturbation method (HPM) to find the travelling wave solutions for some non-linear initial-value problems in the mathematical physics. These problems consist of the Burgers-Fisher equation, the Kuramoto-Sivashinsky equation, the coupled Schordinger KdV equations and the long-short wave resonance equations together with initial conditions. The results of these problems reveal that the HPM is very powerful, effective, convenient and quite accurate to the systems of non-linear equations. It is predicted that this method can be found widely applicable in engineering and physics.

Keywords: homotopy perturbation method; travelling wave solutions; Burgers-Fisher equation; Kuramoto-Sivashinsky equation; coupled Schordinger KdV equations; long-short wave resonance equations

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00036810902943604

Affiliations: 1: Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt,Mathematics Department, Faculty of Science, Taif University, Kingdom of Saudi Arabia 2: Mathematics Department, Faculty of Science, El-Minia University, El-Minia, Egypt,Mathematics Department, Faculty of Science, Taif University, Kingdom of Saudi Arabia

Publication date: 2009-04-01

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