Three-wave interactions, quasipatterns and spatio-temporal chaos in the Faraday Wave experiment

Three-wave interactions form the basis of our understanding of many

nonlinear pattern forming systems because they encapsulate the most basic

nonlinear interactions. In problems with two comparable length scales, such

as the Faraday wave experiment with multi-frequency forcing, consideration

of three-wave interactions can explain the presence of the spatio-temporal

chaos found in some experiments, enabling some previously unexplained

results to be interpreted in a new light. The predictions are illustrated

with numerical simulations of a model partial differential equation.