  The long-wavelength properties of a noisy Kuramoto-Sivashinsky (KS) equation
in 1+1 dimensions are investigated by use of the dynamic renormalization group
(RG) and direct numerical simulations. It is shown that the noisy KS equation
is in the same universality class as the Kardar-Parisi-Zhang (KPZ) equation in
the sense that they have scale invariant solutions with the same scaling
exponents in the long-wavelength limit. The RG analysis reveals that the RG
flow for the parameters of the noisy KS equation rapidly approach the KPZ fixed
point with increasing the strength of the noise. This is supplemented by the
numerical simulations of the KS equation with a stochastic noise, in which the
scaling behavior of the KPZ equation can be easily observed even in the
moderate system size and time.
