Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method

Generalized solitary and periodic wave solutions to a (2+1)-dimensional Zakharov–Kuznetsov equation

“…By a similar approach, from (22) we can obtain compact-like solutions to Eq. (1) in the form u 10;11 ðx; y; tÞ ¼…”

“…Furthermore, the Exp-function method is more applicable to discrete NLEEs than hyperbolic function method. (iv) Instead of involving a sub-equation together with a long list of solutions, it can be applied to other subequations such as Ricatti equations [22], [35], [49][50][51][52]. Moreover, it can be combined with other methods such as the variational iteration method [53].…”

“…For this purpose, some accurate techniques have been presented in the open literature; for example, inverse scattering transform method [1], Jacobi elliptic function method [2], tanh-coth function method [3], sine-cosine function method [4], symmetry method [5], F-expansion method [6], Hirota's bilinear method [7], Painlevé expansion method [8], homogeneous balance method [9], Bäcklund transformation method [10], Adomian decomposition method [11], variational iteration method [12], homotopy analysis method [13], homotopy perturbation method [14] and so on. On the other hand, with the development of computer algebra systems (they allow us to perform the tedious and complicated algebraic calculations on a computer) in recent years, many direct and effective methods using symbolic computation are also presented such as the (G 0 /G)-expansion method [15][16][17][18][19] and the Exp-function method [20][21][22][23][24].…”

On new traveling wave solutions of the Hirota-Satsuma coupled KdV equation

“…We recall that most of these methods use the wave variable transformation to reduce the nonlinear PDE to ODE in order to acquire the solution. Several are tanh [1], G ′ /G-expansion [2], Jacobi elliptic function [3], mapping [4], tanh-sech [5],exp-function [6] and first integral methods [7]. All of these methods are effective methods for acquiring traveling wave solutions NPDE.…”

On soliton solutions of the Wu-Zhang system

“…Most of these methods use the wave variable transformation to reduce the nonlinear partial di erential equation (NPDE) to an ordinary di erential equation (ODE) in order to acquire the soliton solution. Some of these methods are G ′ /G -expansion [2], Jacobi elliptic function [3], inverse scattering [4], Hirota bilinear [5], exp-function [6], and the rst integral [7] methods. There are also e ective studies for acquiring traveling wave solutions of NPDE's [8][9][10][11][12][13][14][15][16][17].…”