The extended F-expansion method and its application for a class of nonlinear evolution equations

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

“…(ii) As mentioned in [40], Jacobi elliptic function method [2] cannot be applied to solve the NLEEs in which the odd and evenorder derivative terms coexist. This observation is also true for tanh-coth function method [3] and F-expansion method [6]. However, in [41], it is shown that the Burgers' equation in which the odd and even-order derivative terms coexist can be solved by the Exp-function method.…”

“…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].…”

Discrete exact solutions to some nonlinear differential-difference equations via the (G′/G)-expansion method

“…Many effective analytic methods for solving nonlinear evolution equations (NEEs) are available in the literature [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. How to extend newly developed methods for NEEs to solve NDDEs is an interesting and important issue.…”

Topological and Non-Topological Soliton Solutions of the Coupled Klein-Gordon-Schrodinger and the Coupled Quadratic Nonlinear Equations

“…Therefore solving nonlinear problems play an important role in nonlinear sciences. Many effective methods of obtaining explicit solutions of NPDEs have been presented such as the tanh-function method and its various extension [1,2], the Jacobi elliptic function expansion method [3], the homogeneous balance method [4], the F-expansion method and its extension [5], ( G ′ G )-expansion method [6], the modified simple equation method [7,8], the semi-inverse variational principle [9] the solitary wave ansatz method [10,11,12,13,14,15,16,17,18,19,20,21] and so on. It is very interesting to note that the solitary wave ansatz method has been successfully applied to many kinds of NLPDEs with constant and varying coefficients, such as, for example, the K(m, n) equation [14,21], the BBM equation [20], the B(m, n) equation [17], the nonlinear Schrodinger's equation [14,18] and many others.…”