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

Abstract

In this paper, using modified -expansion method, we present some explicit formulas of exact traveling wave solutions for the foam drainage equation. A modified -expansion method is proposed by taking full advantages of -expansion method and Riccati equation in seeking exact solutions of non-linear partial differential equations.

Two New Modifications of the Exp-Function Method for Solving the Fractional-Order Hirota-Satsuma Coupled KdV

“…where φðξÞ is satisfied in equation (8). The homogeneous balance between linear and nonlinear terms in each equation of (22) leads to m = 2, n = 1 or 2, and k is arbitrary.…”

“…Recently, the fractional differential equations have become the focus of many scientists in the field of physics and mathematics and also many researchers to focus on this topic [3][4][5][6]. It can provide many methods for obtaining their exact solutions, such as the G ′ /G-expansion method [7][8][9], the exp-function method [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], the homotopy analysis method [29,30], and spectral methods [31][32][33]. And in the meantime, obtaining the exact soliton solutions to these equations is more important because this study gives us a great deal of information on various sciences such as fluid mechanics, physics, and mathematics.…”

Diverse Exact Soliton Solutions of the Time Fractional Clannish Random Walker’s Parabolic Equation via Dual Novel Techniques

“…A modified F-expansion method is proposed by taking full advantages of F expansion method and Riccati equation in seeking exact solutions of nonlinear PDEs. Darvishi and Najafi [39] used a modified F-expansion method to handle the foam Drainage equation. Aasaraai [40] used this method to construct new solutions of the nonlinear ð1 + 2Þ-dimensional Maccari's system.…”

Analytic Solutions of the Kadomtsev-Petviashvili Equation with Power Law Nonlinearity Using the Sine-Cosine Method

“…Therefore solving nonlinear problems plays an important role in nonlinear sciences. Many effective methods of obtaining explicit solutions of NPDEs have been presented such as the tanh-method [1][2][3],the extended tanh method [4][5][6], the sine-cosine method [7][8][9][10], the homogeneous balance method [11], homotopy analysis method [12][13][14][15][16][17][18], the F-expa nsion method [19],three-wave method [20][21][22], extended homoclinic test approach [23][24][25], the (G'/G)-expansion method [26] and the exp-function method [27][28][29][30].…”