Investigations of nonlinear phenomena on the charged surface of liquid hydrogen are reviewed. It is demonstrated that excitation of the surface by a low frequency AC electric field results in the formation of capillary waves in the high-frequency domain, and that the latter exhibit turbulence. The quasi-adiabatic decay of this capillary turbulence has been studied both experimentally and theoretically. It is shown that the processes of formation and decay of the turbulence are both controlled by the same relaxation mechanisms. For spectrally narrow pumping, the application of an additional low-frequency driving force causes a decrease of wave amplitude in the high-frequency domain of the turbulent spectrum and correspondingly decreases the width of the inertial range of energy transfer.