The periodic wave solutions for the Klein–Gordon–Schrödinger equations

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

“…Among of them, (21), (23), and (24) are equivalent to (27), (28), and (29), respectively. However, as demonstrated above, (20) and (22) with an explicit linear function in ξ are different from (27) - (29) and cannot be obtained by the (G /G)-expansion method [25, 26, 28 -31] and its improvements [27,36] if we don't transform (13) into (14) but directly solving (13). In this sense, we may conclude that the modified version proposed in this paper is different from and superior to Wang et al's method [25] if and only if the reduced ODE (4) possesses the property r 1.…”

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.…”

Expanded (G/G2) Expansion Method to Solve Separated Variables for the 2+1-Dimensional NNV Equation

“…For many years people have done a lot of work for this and have achieved a series of important results, such as the Inverse Scattering Transformation(IST) [1], Darboux transform [2,3], Lie group and nonclassical Lie group method [4,5], Hirota bilinear method [6][7][8], and other important methods. Among them, the function expansion [9][10][11][12][13][14][15][16][17][18][19] has the advantages of simplicity, directness, and ease of operation. So there is a lot of use in solving nonlinear partial differential equations.…”