(6)New applications of the two variable ( G / G , 1/ G )-expansion method for closed form traveling wave solutions of integro-differential equations
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M. Mamun Miah a,e, H.M. Shahadat Ali b,e, M. Ali Akbar c,e, Aly R. Seadawy d,e,*
a Department of Mathematics, Khulna University of Engineering and Technology, Bangladesh
b Department of Applied Mathematics, Noakhali Science and Technology University, Bangladesh
c Department of Applied Mathematics, University of Rajshahi, Bangladesh
d Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
e Department of Mathematics, Faculty of Science, Beni-Suef University, Egypt
Received 17 February 2019; received in revised form 5 March 2019; accepted 5 March 2019
Available online 23 March 2019
Abstract
Most fundamental themes in mathematical physics and modern engineering are investigated by the closed form traveling wave solutions
of nonlinear evolution equations. In our research, we ascertain abundant new closed form traveling wave solution of the nonlinear integro-
differential equations via Ito equation, integro-differential Sawada–Kotera equation, first integro-differential KP hierarchy equation and second integro-differential KP hierarchy equation by two variable ( G, / G, 1/ G )-expansion method with the help of computer package like Mathematica. Some shape of solutions like, bell profile solution, anti-king profile solution, soliton profile solution, periodic profile solution etc. are obtain in this investigation. Trigonometric function solution, hyperbolic function solution and rational function solution are established by using our eminent method and comparing with our results to all of the well-known results which are given in the literature. By means of free parameters, plentiful solitary solutions are derived from the exact traveling wave solutions. The method can be easier and more applicable to investigate such type of nonlinear evolution models.
© 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: The two variable ( G,/ G, 1/ G )-expansion method; Travelling wave solutions; Integro-differential ito equation; Integro-differential Sawada–Kotera equation; First integro-differential KP hierarchy equation; Second integro-differential KP hierarchy equation.