Amplitude equations for Rayleigh-Bénard convective rolls far from threshold

An extension of the amplitude method is proposed. An iterative algorithm is developed to build an amplitude equation model that is shown to provide precise quantitative results even far from the linear instability threshold. The method is applied to the study of stationary Rayleigh-Bénard thermoconvective rolls in the nonlinear regime. In particular, the generation of second and third spatial harmonics is analyzed. Comparison with experimental results and direct numerical calculations is also made and a very good agreement is found.