Coherent structures in convection and parametrically driven surface waves

A system maintained outside of thermodynamic equilibrium often develops complex spatial structures and, in some cases, persistent dynamics. The amplitude equation formalism has been widely used to study pattern formation in the weakly nonlinear regime (slightly beyond onset of instability from some stationary reference state.) Application of the formalism is briefly discussed for Rayleigh-Benard convection, and at some length for parametrically driven surface waves (Faraday waves).