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A Generalized Tanh-Function Type Method and the(G'/G) -Expansion Method for Solving  [PDF]
Weimin Zhang
Applied Mathematics (AM) , 2013, DOI: 10.4236/am.2013.410A1003
Abstract: In this paper a generalized tanh-function type method is proposed by using the idea of the transformed rational function method. We show that the (G'/G) -expansion method is a special case of the generalized tanh-function type method, so the (G'/G) -expansion method is considered as a special deformation application of the transformed rational function method. We demonstrate that all solutions obtained by the (G'/G) -expansion method were found by the generalized tanh-function type method. As applications, we consider mKdV equation. Compared with the (G'/G) -expansion method, the generalized tanh-function type method gives new and more abundant solutions.
The (ω/g)-expansion method and its application to Vakhnenko equation
中国物理 B , 2009,
Abstract: This paper presents a new function expansion method for finding travelling wave solutions of a nonlinear evolution equation and calls it the (ω/g)-expansion method, which can be thought of as the generalization of (G'/G)-expansion given by Wang et al recently. As an application of this new method, we study the well-known Vakhnenko equation which describes the propagation of high-frequency waves in a relaxing medium. With two new expansions, general types of soliton solutions and periodic solutions for Vakhnenko equation are obtained.
New application of the (G'/G,1/G)-expansion method to the KP equation
Yun-Jie Yang,Yan He
Applied Mathematical Sciences , 2013,
Abstract: In this paper, we extend the (G'/G,1/G)-expansion method to the (2+1)-dimensional Kadomstev-Petivshvili (KP) equation. As a result, hyperbolic function solution, trigonometric function solution and rational solution are obtained.
Modified $(G'/G)$-expansion method for solving nonlinear partial differential equations  [PDF]
Mahouton Norbert Hounkonnou,Rolland Finangnon Kanfon
Physics , 2013,
Abstract: This paper addresses a modified ($G'/G$)-expansion method to obtain new classes of solutions to nonlinear partial differential equations (NPDEs). The cases of Burgers, KdV and Kadomtsev-Petviashvili NPDEs are exhaustively studied. Relevant graphical representations are shown in each case.
Exact Solutions of the BBM and MBBM Equations by the Generalized (G'/G )-expansion Method Equations
International Journal of Genetic Engineering , 2012, DOI: 10.5923/j.ijge.20120203.02
Abstract: In this article, we establish exact solutions for the BBM and the MBBM equations by using a generalized (G'/G )-expansion method. The generalized (G'/G )-expansion method was used to construct solitary wave and periodic wave solutions of nonlinear evolution equations. This method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that the (G'/G )-expansion method is straightforward and powerful mathematical tool for solving nonlinear problems.
The (G`/G)-Expansion Method for Traveling Wave Solutions of Burgers’ Kdv and Generalization of Huxley Equations
American Journal of Computational and Applied Mathematics , 2012, DOI: 10.5923/j.ajcam.20120203.09
Abstract: The (G`/G)-expansion method is used for determining the exact traveling wave solutions of the Burgers-KdV and generalization of Huxley equations. The obtained solutions are compared with the solutions found by Wazwaz[18]. The (G`/G)-method is very powerful and easy tool for solving non-linear partial differential equations
Exact solutions for the general fifth order KdV equation by the extended tanh method  [PDF]
Alvaro Salas,Cesar A. Gomez S.,Jose Gonzalo Escobar Lugo
Physics , 2008,
Abstract: In this paper we show some exact solutions for the general fifth order KdV equation. These solutions are obtained by the extended tanh method.
An Innovative Solutions for the Generalized FitzHugh-Nagumo Equation by Using the Generalized (G'/G)-Expansion Method  [PDF]
Sayed Kahlil Elagan, Mohamed Sayed, Yaser Salah Hamed
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.24060
Abstract: In this paper, the generalized (G'/G)-expansion method is used for construct an innovative explicit traveling wave solutions involving parameter of the generalized FitzHugh-Nagumo equation , for some special parameter where satisfies a second order linear differential equation , , where and are functions of .
Solving the Burgers-Huxley Equation by G'/G Expansion Method  [PDF]
Mingxing Zhu
Journal of Applied Mathematics and Physics (JAMP) , 2016, DOI: 10.4236/jamp.2016.47146
Abstract: By introducing and extending the G'/G expansion method with the aid of computer algebraic system “Mathematics”, the exact general solutions were obtained for the Burgers-Huxley equation and special form. Final results were represented in hyperbolic function, trigonometric function and rational function with arbitrary parameters.
Exact Solutions of Gardner Equations through tanh-coth Method  [PDF]
Lin Lin, Shiyong Zhu, Yinkang Xu, Yubing Shi
Applied Mathematics (AM) , 2016, DOI: 10.4236/am.2016.718186
Abstract: In this paper, we apply the tanh-coth method and traveling wave transformation method for solving Gardner equations, including (1 + 1)-Gardner and (2 + 1)- Gardner equations. The tanh-coth method proved to be reliable and effective in handling a large number of nonlinear dispersive and disperse equations. Through tanh-coth method, we get analytical expressions of soliton solutions of Gardner equations. The one-soliton solution is characterized by an infinite wing or infinite tail.
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