Abstract
This article reviews recent developments of experimental and theoretical studies of standing surface waves excited by vertical periodic oscillation. Nonlinear phenomena in Faraday surface waves such as low-dimensional chaos of mode-competition, anomalous diffusion of floating particles on the surface, excitation of one-dimensional parametric solitary waves, two-dimensional pattern selection and associated spatiotemporal modulation have been found and investigated vigorously. Especially, spontaneous formation of various patterns on parametrically excited surface waves under different experimental conditions is explained and a theory based on Lyapunov functional method is applied to this problem.
