Propagations of symmetric bidirectional nonlinear waves in two-mode foam drainage model

Abstract

In this paper, a new two-mode version of the foam drainage equation is presented. The new model describes the motion of instantaneous symmetric double-waves and their interaction depends on two involved parameters known as nonlinearity and phase-velocity. Two recent methods are used to obtain solutions with interesting variety of physical structures such as kink-type and periodic shape. In addition, the influence of both nonlinearity and phase-velocity parameters are investigated by using graphical analysis. Finally, all the obtained solutions to the TMFD are confirmed by direct substituting and verifying the correctness of the governing equation.

Keywords

• Two-mode foam drainage equation
• Rational sine–cosine method
• Rational sinh–cosh method