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Lenells, J. 2005. Traveling wave solutions of the Camassa-Holm equation, J. Diff. Eq. 217: 393-430.

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Article

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

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


American Journal of Applied Mathematics and Statistics. 2015, Vol. 3 No. 1, 23-28
DOI: 10.12691/ajams-3-1-5
Copyright © 2015 Science and Education Publishing

Cite this paper:
Hasibun Naher, 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.

Correspondence to: Hasibun  Naher, Department of Mathematics and Natural Sciences, BRAC University, Mohakhali, Dhaka, Bangladesh. Email: hasibun06tasauf@gmail.com

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.

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