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.