Investigating bifurcations of spatial wave regimes in the vicinity of special resonance points on the surface of a viscous liquid film flowing down a vertical cylinder

The flows of a viscous liquid film along the outer surface of a vertical cylinder are considered. The study employs a model nonlinear evolutionary equation for film thickness deviation from the undisturbed level. It is valid for describing long-wave perturbations in the case of small fluid flows and large cylinder radii. The branching of spatial wave regimes from the undisturbed flow regime is investigated. Particular attention is paid to special cases when the values of the radii of the cylinders lie in the vicinity of some specific critical points. To study such cases, a model system of equations is obtained from the initial equation. Several solutions of this system are given.