Modified simple equation method for nonlinear evolution equations

The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method

“…For a large class of equations of the type represented in (3.1), the exact solution can be assumed to be in the form of (3.2) where and must be an integer; are parameters; [20] pointed out that the solution method is equivalent to tanh-coth method, and so the derived exact solutions of the KdV equation will be the same as those given in equations (2.1-8).…”

“…The simplest equation method [14][15][16][17][18][19][20] is a method commonly used to develop the exact solutions of some ordinary nonlinear differential equations. Here, the method is applied to develop exact solutions of the KdV equation.…”

Exact Solutions to the (2+1)-Dimensional Boussinesq Equation via exp(?(?))-Expansion Method

“…complex hyperbolic function method [5,6], the rank analysis method [7], the ansatz method [8,9], the (G′/G)-expansion method [10][11][12][13][14][15][16][17][18][19][20][21], the exp-functions method [22], the modified simple equation method [23,24], the Jacobi elliptic function expansion method [25,26], the Adomian decomposition method [27,28], the homogeneous balance method [29][30][31], the F-expansion method [32,33], the Backlund transformation method [34], the Darboux transformation method [35], the homotopy perturbation method [36,37], the generalized Riccati equation method [38], the tanh-coth method [39], the exp(-φ(η))-expansion method [40][41][42][43] and so on.…”

Application of an Enhanced (G’/G)-Expansion Method to Find Exact Solutions of Nonlinear PDEs in Particle Physics

“…Many powerful method have been obtainable for instance the exp(-Φ(ξ))-expansion method (Khan et al, 2013a;Islam et al, 2014); the jacobi elliptic function method (Ali, 2011); the homogeneous balance method (Wang, 1995;Zayed et al, 2004); the modified simple equation method (Jawad et al, 2010;Khan and Akbar, 2013b;Zayed and Ibrahim, 2012;Akter and Akbar, 2015); the (G′/G)-expansion method (Wang et al, 2008;Zayed, 2010;Akbar et al, 2012b;Zayed and Gepreel, 2009;Akbar and Ali, 2011;Shehata, 2010;Akbar et al, 2012a;Mirzazadeh et al, 2014;; the improve (G′/G)-expansion method (Zhang et al, 2010); the extended(G′/G)-expansion method (Roshid et al, 2014a;; the generalized (G′/G)-expansion method 2014c); the novel (G′/G)-expansion method (Hafez et al, 2014); the homotopy perturbation method (Mohyud-Din et al, 2011a;2011b;2011c); the variational method (He, 1997;Abbasbandy, 2007;Arife and Yildirim, 2011;Abdou and Soliman, 2005); the exp-function method (Akbar and Ali, 2012;He and Wu, 2006;Naher et al, 2012); the truncated painleve expansion method (Weiss et al, 1983); the asymptotic method (He, 2008); the Hirota's bilinear transformation method (Hirota, 1973;Hirota and Satsuma, 1981); the tanhfunction method (Abdou, 2007;…”