Subcritical bifurcations and nonlinear balloons in faraday waves

Abstract

Bicritical points at wave numbers k(b) larger than the critical wave numbers k(c) are found in parametric surface waves (Faraday waves) using both numerical simulations and nonlinear analysis. Because k(b)-k(c) is small, it is argued that subcritical bifurcations at k>k(b) can be easily observed in experiments. In the second part we present a generic argument predicting the existence of nonlinear states resembling a balloon outside the instability region. The prediction is confirmed in simulations and it is argued to apply to other systems with similar instability curves.