Faraday resonance in two-dimensional standing gravity waves of finite depth

Faraday waves arise on the surface of a liquid in a container that is undergoing vertical periodic oscillations. The motion of two resonant modes with natural frequencies in the approximate ratio 3:1 is considered in this paper. We derive the nonlinear evolution equations of the dominant free-surface modes up to fifth-order in wave amplitude. It is found that the third-order evolution equations are integrable while the fifth-order evolution equations are chaotic, which shows that the fifth-order nonlinearity breaks the integrability of the third-order integrable system.