Studying evolution of periodic wave regimes on a falling down liquid film

The numerical simulation of wavy regimes of the freely-falling liquid film was realized using the previously discovered symmetry of model equations. The calculation results are presented for the dynamics of amplitudes of significant harmonics and for the wave surface evolution.The paper has resulted in finding a specific regime, characterized by an alternate predominance of the first and second harmonics. At certain values of parameters this limiting cycle may have a very large period, during which the solution is attracted to the quasi-steady-state traveling regime, then suddenly transforms, and again tends to the quasi-steady-state with a phase shift of a half wave length.