Application of Linear ODE as Auxiliary Equation to the Nonlinear Evolution Equation

Hasibun Naher^1, and Fardousi Ara Begum¹

¹Department of Mathematics and Natural Sciences, BRAC University, Mohakhali, Dhaka, Bangladesh

Cite this paper:
Hasibun Naher and Fardousi Ara Begum. Application of Linear ODE as Auxiliary Equation to the Nonlinear Evolution Equation. American Journal of Applied Mathematics and Statistics. 2015; 3(1):23-28. doi: 10.12691/ajams-3-1-5

Abstract

In this article, simplified Modified Camassa-Holm (SMCH) equation is investigated to construct some new analytical solutions via the improved (G’/G)-expansion method. Second order linear ordinary differential equation is used with constant coefficients in the method. As a result, some new travelling wave solutions are obtained through the hyperbolic function, the trigonometric function and the rational forms. If parameters take specific values, the solitary waves are derives from the travelling waves. Furthermore, some of the solutions are presented in the figures with the aid of commercial software Maple.

Keywords:
The SMCH equation analytical solutions nonlinear partial differential equation ordinary differential equation auxiliary equation the improved (G’/G)-expansion method

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Figures

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