Study of exp(-Φ(ξ))-expansion Method for Solving Nonlinear Partial Differential Equations
S. M. Rayhanul Islam
Department of Mathematics, Pabna University of Science and Technology, Pabna-6600, Bangladesh.
Kamruzzaman Khan *
Department of Mathematics, Pabna University of Science and Technology, Pabna-6600, Bangladesh.
M. Ali Akbar
Department of Applied Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh.
*Author to whom correspondence should be addressed.
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.
Keywords: exp(-Φ(ξ))-expansion method, the Gardner equation, NPDEs, exact solutions.