Amplitude Equations from Spatiotemporal Binary-Fluid Convection Data

We apply a recently developed method for the analysis of spatiotemporal data to extract the dynamical equations that describe an experiment on traveling-wave convection in a binary fluid. The technique is based on nonlinear regression analysis and allows the nonparametric estimation of the functions involved in these equations. We find that the system is well described by a pair of coupled complex Ginzburg-Landau equations, and the coefficient of the term that describes the interaction between the two oppositely propagating waves can be determined.