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

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

Acknowledgements

The authors wish to thank the referees for their suggestions and comments.