## Large-scale statistics of the Kuramoto-Sivashinsky equation: A wavelet-based approach

We show that the statistical properties of the large scales of the Kuramoto-Sivashinsky equation in the extended system limit can be understood in terms of the dynamical behavior of the same equation in a small finite domain. Our method relies on the description of the solutions of this equation in terms of wavelets, and allows us to model the energy transfer between small and large scales. We show that the effective equation obtained in this way can be consistently approximated by a forced Burgers equation only for scales far from the cutoff between small and large wavelengths. {copyright} {ital 1996more »