Exact traveling wave solutions of nonlinear variable-coefficients evolution equations with forced terms using the generalized ( G′/G)-expansion method

Exact Traveling Waves of a Generalized Scale-Invariant Analogue of the Korteweg–de Vries Equation

“…There are many known powerful methods that can be used to find the exact solutions of nonlinear partial differential equations, such as Hirota's bilinear method [2], the inverse scattering transform method [1], the ( G G )-expansion method [15,16], the Riccati-Bernoulli sub-ODE method [17,18], the homogeneous balance method [19], and the generalized Riccati equation mapping method [20,21]. Other recent meritorious work on finding exact solutions include [22][23][24][25][26][27][28].…”

The Jacobi Elliptic Equation Method for Solving Fractional Partial Differential Equations

“…The powerful and efficient methods to find analytic solutions and numerical solutions of nonlinear equations have drawn a lot of interest by a diverse group of scientists. Many efficient methods have been presented so far (e.g., see [1][2][3][4][5][6][7][8][9]). Fractional differential equations are generalizations of classical differential equations of integer order.…”

Exact Solutions for the Nonlinear (2+1)-Dimensional Davey-Stewartson Equation Using the Generalized $(\frac{G'}{G})$-Expansion Method

“…These exact solutions of these NLPDEs are important for the understanding of the nonlinear physical phenomena and possible applications. In the past several decades, many effective methods for obtaining exact solutions of NLPDEs have been presented, such as the tanh function method (Fan, 2000;El-Wakil et al, 2007), the tanh-sech method (Malfliet et al, 1996;Wazwaz, 2004), the sine-cosine method (Al-Mdallal et al, 2007;Zayed & Abdelaziz, 2011), the homogeneous balance method (Fan et al, 1998), the Jacobi elliptic function method (Dai et al, 2006), the F-expansion method (Zhang et al, 2006), the homotopy perturbation method (He, 2005), the inverse scattering transformation method (Ablowitz et al, 1981), the Bäcklund transformation method (Miura, 1978), the Hirota bilinear method (Hirota, 1973), the exp-function method Zayed et al, 2012), the ( G G )-expansion method (Wang et al, 2008;Zayed & Abdelaziz, 2010, 2013 and so on. Very recently, Wang et al (2008) introduced an expansion technique called the ( G G )-expansion method and they demonstrated that it was a powerful technique for seeking analytic solutions of NLPDEs.…”