Journal of Ocean Engineering and Science

Volume 2, Issue 1

(6)Abundant general solitary wave solutions to the family of KdV type equations

Md. Azmol Huda ^a , M. Ali Akbar ^{b ,}^∗, Shewli Shamim Shanta ^c‍‍‍a Mathematics Discipline, Khulna University, Khulna, Bangladesh ‍‍‍‍‍‍‍

‍‍‍‍‍‍‍b Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh

c Department of Mathematics, University of Rajshahi, Rajshahi, Bangladesh

Received 4 November 2016; received in revised form 7 January 2017; accepted 6 February 2017
Available online 1 March 2017‍‍‍‍

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Abstract
This work explores the construction of more general exact traveling wave solutions of some nonlinear evolution equations (NLEEs)
through the application of the ( G / G , 1/ G )-expansion method. This method is allied to the widely used ( G / G )-method initiated by Wang et al. and can be considered as an extension of the ( G / G )-expansion method. For effectiveness, the method is applied to the family of KdV type equations. Abundant general form solitary wave solutions as well as periodic solutions are successfully obtained through this method. Moreover, in the obtained wider set of solutions, if we set special values of the parameters, some previously known solutions are revived. The approach of this method is simple and elegantly standard. Having been computerized it is also powerful, reliable and effective.
© 2017 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Keywords: Nonlinear evolution equation; Solitary wave solution; Potential KdV equation; Complex modified KdV equation.