New periodic solutions for nonlinear evolution equations using Exp-function method

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

“…(1) are the same as (23) and (20), respectively. Similarly, if we apply the transformations (25) to (57) and (58) and take b 0 = 5/2, then we get periodic wave solutions to Eq.…”

“…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].…”

New Exact Solutions of Some Nonlinear Evolution Equations by Sub-Ode Method

“…Thus the methods for deriving exact solutions for the governing equations have to be developed. Many powerful methods are used to obtain travelling solitary wave solutions to nonlinear partial differential equations (PDEs) such as tanh method [12,13], the ansatz method [5,6], the sub-ODE method [3,4], Jacobi elliptic function method [1], exp-function method [7,8] and so on.…”

Numerical Solution Of 12th Order Boundary Value Problems By Using Homotopy Perturbation Method

“…Recently various powerful mathematical methods such as variational iteration method [14][15][16][17][18][19][20][21][22][23], exp-function method [24][25], f-expansion method [24], this paper, applies the homotopy perturbation method (HPM) [1][2][3][4][5].…”