An analysis of analytic and approximate solutions of the nonlinear foam-drainage equation and its applications

Abstract

In this study, the modified Kudryashov and Riccati-Bernoulli (sub-ODE) methods are applied to construct some analytical solutions of the nonlinear Foam-drainage equation which plays an important part in the formation and evolution of liquid foams. Kink type, singular and logarithmic function solutions are obtained. Then, the residual power series method (RPSM) is used to analyze the numerical behavior of the equation by considering all the exact solutions. We observed that the modified Kudryashov and Riccati Bernoulli sub-ODE methods are powerful techniques for finding the exact solutions to various nonlinear models. Also, the RPSM is efficient for examining numerical behavior of nonlinear models. Some interesting figures are shown to show the reliability of the methods.