J. Elezgaray et al., LARGE-SCALE STATISTICS OF THE KURAMOTO-SIVASKINSKY EQUATION - A WAVELET-BASED APPROACH, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 54(1), 1996, pp. 224-230
We show that the statistical properties of the large scales of the Kur
amoto-Sivashinsky equation in the extended system limit can be underst
ood 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 ener
gy transfer between small and large scales. We show that the effective
equation obtained in this way can be consistently approximated by a f
orced Burgers equation only for scales far from the cutoff between sma
ll and large wavelengths.