Application of Exp-function method to high-dimensional nonlinear evolution equation

Exp-Function Method for N-Soliton Solutions of Nonlinear Differential-Difference Equations

“…where ξ i = k i n + c i t + w i (i = 1, 2, 3), and It is easy to see that (36) -(38) have the same form as (15) - (17). By the similar manipulations mentioned above, we have…”

Exp-Function Method with Computerized Symbolic Computation for New Exact Solution of Burger's Equation

“…For the comparison between solutions (11) and (12), we use Fig. 2 to show a spatial structure of solution (12) by selecting 1 w = and letting the other parameters be same as those in Fig. 1. (a) [ 5,5], Fig.…”

“…2. Spatial structure of solution (12) From Figs. 1 and 2, we can see that solutions obtained by the improved exp-function method in present paper may have new spatial structures besides the spatial structures determined by the solutions constructed by the exp-function method [1].…”

“…Among the existing methods, the exp-function method [1] proposed by He and Wu in 2006 is a simple and direct method for nonlinear PDEs. More importantly, the exp-function method and its improvements are available for many PDEs such as those in [9][10][11][12][13][14][15][16], this is due to the method possesses a more general ansätz [17]: …”

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

“…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...…”