Renormalization-group analysis of a noisy Kuramoto-Sivashinsky equation

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Abstract
We have analyzed the Kuramoto-Sivashinsky equation with a stochastic noise term through a dynamic renormalization-group calculation. For a system in which the lattice spacing is smaller than the typical wavelength of the linear instability occurring in the system, the large distance and long-time behavior of this equation is the same as for the Kardar-Parisi-Zhang equation in one and two spatial dimensions. For the d=2 case the agreement is only qualitative. On the other hand, when coarse graining on larger scales the asymptotic flow depends on the initial values of the parameters.
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