Nonlinear stability of the flat-surface state in a Faraday experiment

Faraday first observed the onset of waves on the surface of a horizontal layer of fluid subjected to a vertical oscillation [5]. This phenomenon has been widely studied both theoretically and experimentally due to the plethora of patterns that may be observed depending on the parameters of the problem, such as the frequency of oscillations, the viscosity of the fluid, or the depth of the layer (see, e.g., [4], [12], [19]).