New solitary wave and periodic solutions of the foam drainage equation using the Exp-function method

Traveling Wave Solutions for Foam Drainage Equation by Modified F-Expansion Method

“…setting = 2 k c yields the same solution (20) of [28] which is also in agreement with the selection for the solutions in [27,29].…”

“…Hellal and Mehanna [27] used a Food and Public Health 2012; 2(1): 6-10 7 semi-analytical method, that is the Adomian decomposition and the tanh method to handle the foam drainage equation (1). Also, equation (1) was studied by another authors using different methods, such as the exp-function method [28], self-similar technology [29], homotopy analysis method [30] and the variational approach [31]. In this paper, we will apply the F -expansion method on foam drainage equation (1).…”

He's Semi-inverse Method for Camassa-Holm Equation and Simplied Modied Camassa-Holm Equation

“…Also, the explicit formulas may provide physical information and help us to understand the mechanism of related physical models. Recently, many kinds of powerful methods have been proposed to find exact solutions of nonlinear partial differential equations, e.g., the tanh-method [1], the homogeneous balance method [2], homotopy analysis method [3,4,5,6,7,8,9], the F −expansion method [10], three-wave method [11,12,13], extended homoclinic test approach [14,15,16], the ( G G )−expansion method [17] and the exp-function method [18,19,20,21,22]. The outline of the present paper is as follows.…”

Application of Multiple Exp-Function Method to Obtain Multi-Soliton Solutions of (2 + 1)- and (3 + 1)-Dimensional Breaking Soliton Equations

“…Also, the explicit formulas may provide physical information and help us to understand the mechanism of related physical models. Recently, many kinds of powerful methods have been proposed to find exact solutions of nonlinear partial differential equations, e.g., the tanh-method [1], the homogeneous balance method [2], homotopy analysis method [3][4][5][6][7][8], the F − expansion method [9], three-wave method [10][11][12][13], extended homoclinic test approach [14][15][16], the ( ) G G ′ − expansion method [17] and the exp-function method [18][19][20][21][22][23].…”