Dynamical behaviour of the foam drainage equation

Abstract

In this study, we examine the well-known foam drainage equation in the form of the nonlinear partial differential equation using a new extended direct algebraic method. This remarkable powerful method transforms the equation under study into an ordinary differential equation using a wave transformation which provides an exact form to the problem considered in the paper. Graphical representation for the acquired solution is presented through 3-D plots which variable parameters to show the efficiency and simplicity of the method used. From these plots, the methods prove to be a reliable and effective approach for solving nonlinear similar problems and can be accounted for in the near future for possible application to similar models.