Nonlinear dynamics of Faraday waves at the surfactant-covered free surface of the vertically vibrated liquid layer

In our previous paper (Fluid Dyn. Res., vol. 48 (2016), 061403) we studied the influence of the solutocapillary effect due to absorbed insoluble surfactant and thermocapillary effect caused by heating on the generation of Faraday waves. The problem was considered in the framework of linear theory and Floquet method for the semi-infinite liquid layer, as well as for the layer with finite depth. Within the Faraday experiment a rich variety of complex patterns are seen, some of which have a complicated spatial structure, but are time-periodic with the periodicity of the driving force, and some have both complicated spatial and temporal structure. Here we propose a weakly nonlinear analysis of the generation of Faraday waves.