Analytic study on two nonlinear evolution equations by using the (G′/G)-expansion method

Abstract

a b s t r a c tThe validity and reliability of the so-called (G 0 /G)-expansion method is tested by applying it to two nonlinear evolutionary equations. Solutions in more general forms are obtained. When the parameters are taken as special values, it is observed that the previously known solutions can be recovered. New rational function solutions are also presented. Being concise and less restrictive, the method can be applied to many nonlinear partial differential equations.

The Modified (G'/G)-Expansion Method for Nonlinear Evolution Equations

“…It is easy to see that (32) is equivalent to (31), however, (30) cannot be obtained from (27). (20) and (21) can be respectively simplified as…”

Modified Simple Equation Method and its Applications for some Nonlinear Evolution Equations in Mathematical Physics

“…The solution of Eq. (3.20) has been investigated by using other methods via the modified variational iteration method [33], the variational homotopy perturbation method [34] and the (G'/G )-expansion method [28]. Let …”

“…Because of the increased concentration in the theory of solitary waves, a large variety of analytic and computational methods have been established in the analysis of the nonlinear models. For example the inverse scattering transformation method [1], the Hirota bilinear transform method [2], the Painleve integration method [3][4][5][6], the Backlund transformation method [7,8], the exp-function method [9][10][11][12][13], the tanh-function method [14][15][16][17], the Jacobi-elliptic function expantion method [18][19][20], the (G'/G)-expansion method [21][22][23][24][25][26][27][28][29], the (G'/G,1/G)-expansion method [30,31], the first integral method [32], the variational iteration method [33], the homotopy perterbation method [34], the modified simple equation method [35][36][37][38][39] and so on. Recently, Jawad et al [35], Zayed [36] and Zayed et al [37][38][39] have employed the modified simple equatio...…”

The discrete (G′/G)‐expansion method applied to the differential‐difference Burgers equation and the relativistic Toda lattice system

“…Right after their pioneer work, the (G /G)-expansion method became popular in the research community, and a number of studies refining the initial idea have been published [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. The value of the (G /G)-expansion method is that one treats nonlinear problems by essentially linear methods.…”