Instabilities and nonlinear waves in two-layer film flowing down a vertical plane

The two-layer falling film flowing down a vertical plane is considered. The approximate long-wave model is investigated and the integral method is applied on this model. The linear stability of the steady flow is analyzed by the numerical method. To calculate the steady-traveling nonlinear waves we reformulate the problem as the dynamical system and find the bifurcating solutions. Examples of solutions at real-life values of the similarity parameters for a two-layer film are shown.