Modeling nonlinear wave regimes in a falling liquid film entrained by a gas flow

The article studies nonlinear waves on a liquid film, flowing under the action of gravity in a known stress field at the interface. In the case of small Reynolds numbers, the problem is reduced to solving a nonlinear integro-differential equation for the film thickness deviation from the undisturbed level. The nature of branching of wave modes of the unperturbed flow with a flat interface has been investigated. The steady-state traveling solutions with wave numbers that are far enough from the neutral ones, have been numerically found. Using methods of stability theory, the analysis of branching of new families of steady-state traveling solutions has been performed. In particular, it is shown that, similarly to the case of the falling film, this model equation has solutions in the form of solitons-humps.