(9)Further investigations to extract abundant new exact traveling wave solutions of some NLEEs
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M. Mamun Miah a, Aly R. Seadawy b, c, ∗, H.M. Shahadat Ali d, M. Ali Akbar e
a Department of Mathematics, Khulna University of Engineering and Technology, Bangladesh
b Mathematics Department, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
c Department of Mathematics, Beni-Suef University, Egypt
d Department of Applied Mathematics, Noakhali Science and Technology University, Bangladesh
e Department of Applied Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh
Received 5 May 2019; received in revised form 20 June 2019; accepted 21 June 2019
Available online 4 July 2019
Abstract
In this study, we implement the generalized ( G'/ G )-expansion method established by Wang et al. to examine wave solutions to some nonlinear evolution equations. The method, known as the double ( G'/ G, 1/ G )-expansion method is used to establish abundant new and further general exact wave solutions to the (3 + 1)-dimensional Jimbo–Miwa equation, the (3 + 1)-dimensional Kadomtsev–Petviashvili equation and symmetric regularized long wave equation. The solutions are extracted in terms of hyperbolic function, trigonometric function and rational function. The solitary wave solutions are constructed from the obtained traveling wave solutions if the parameters received some definite values. Graphs of the solutions are also depicted to describe the phenomena apparently and the shapes of the obtained solutions are singular periodic, anti-kink, singular soliton, singular anti-bell shape, compaction etc. This method is straightforward, compact and reliable and gives huge new closed form traveling wave solutions of nonlinear evolution equations in ocean engineering.
© 2019 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: Exact traveling wave solutions; ( G' / G, 1/G)-expansion method; (3 + 1)-dimensional Jimbo–Miwa equation; (3 + 1)-dimensional Kadomtsev–Petviashvili equation; Symmetric regularized long wave equation.