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Tracy-Widom and Baik-Rains distributions appear as universal limitdistributions for height fluctuations in the one-dimensionalKardar-Parisi-Zhang (KPZ) \textit{stochastic} partial differential equation(PDE). We obtain the same universal distributions in the spatiotemporallychaotic, nonequilibrium, but statistically steady state (NESS) of theone-dimensional Kuramoto-Sivashinsky (KS) \textit{deterministic} PDE, bycarrying out extensive pseudospectral direct numerical simulations to obtainthe spatiotemporal evolution of the KS height profile $h(x,t)$ for differentinitial conditions. We establish, therefore, that the statistical properties ofthe 1D KS PDE in this state are in the 1D KPZ universality class.

The one-dimensional Kardar-Parisi-Zhang and Kuramoto-Sivashinsky universality class: limit distributions