A small-mode model for spatial regimes on a freely falling liquid film

Spatial wave modes of a viscous liquid film freely flowing down a vertical wall are considered. In the case of small Reynolds numbers the problem is reduced to considering solutions of a nonlinear equation for the film thickness deviation from the undisturbed level. It was used to obtain a model system of equations, describing spatially periodic solutions with wave numbers lying in the vicinity of special resonance points and symmetric in the transverse coordinate. Several solutions for this system are provided.