A series solution of the foam drainage equation

Abstract

a b s t r a c tFoaming occurs in many distillation and absorption processes. The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. In this paper, we apply an analytic technique, namely the homotopy analysis method (HAM) to handle the foam drainage equation. The powerful homotopy analysis method computes the solution in a rapidly convergent infinite series. We also compare the numerical results obtained by HPM or ADM and the same results obtained by using the analytic solutions obtained by HAM.

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

“…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 variational method for a (2 + 1)-dimensional soliton equation

“…In recent years, various effective methods have been developed to find the exact solutions of NPDEs, such as tanh-function method [4,5,6,7,8,9,10,11], generalized hyperbolic function method [12], homogeneous balance method [13,14], Jacobi-elliptic function method [15,16,17], exp-function method [18,19], auxiliary equation method [20,21,22,23,24] and so on, e.g. see [25,26,27]. …”

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.…”