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The travelling wave solutions for non-linear initial-value problems using the homotopy perturbation method
Faculty
Science
Year:
2009
Type of Publication:
Article
Pages:
617-634
Authors:
Zayed, E. M. E, Nofal, T. A, Gepreel, K. A
DOI:
10.1080/00036810902943604
Journal:
APPLICABLE ANALYSIS TAYLOR \& FRANCIS LTD
Volume:
88
Research Area:
Mathematics
ISSN
ISI:000267074100009
Keywords :
homotopy perturbation method, travelling wave solutions, Burgers-Fisher equation, Kuramoto-Sivashinsky equation, coupled Schordinger KdV equations, long-short wave resonance equations
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.
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