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Research Article Open access CC BY 4.0

Study of exp(-Φ(ξ))-expansion Method for Solving Nonlinear Partial Differential Equations

S. M. Rayhanul Islam, Kamruzzaman Khan, M. Ali Akbar

Journal of Advances in Mathematics and Computer Science · pp. 397–407 · Published 14 Nov 2014

10.9734/BJMCS/2015/13387

Abstract

In this work we study the Gardner equation or the combined KdV-mKdV equation. We use the exp(-Φ(ξ))-expansion method for a reliable treatment to establish exact traveling wave solutions then the solitary wave solutions for the aforementioned nonlinear partial differential equation (NPDEs). As a result, the traveling wave solutions are obtained in four arbitrary functions including hyperbolic function solutions, trigonometric function solutions, exponential function solutions, and rational function solutions.

exp(-Φ(ξ))-expansion method the Gardner equation NPDEs exact solutions.

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