Tracy-Widom and Baik-Rains distributions appear as universal limit distributions for height fluctuations in the one-dimensional Kardar-Parisi-Zhang (KPZ) stochastic partial differential equation (PDE). We obtain the same universal distributions in the spatiotemporally chaotic, nonequilibrium, but statistically steady state of the one-dimensional Kuramoto-Sivashinsky (KS) deterministic PDE, by carrying out extensive pseudospectral direct numerical simulations to obtain the spatiotemporal evolution of the KS height profile $h(x,t)$ for different initial conditions. We establish, therefore, that the statistical properties of the one-dimensional (1D) KS PDE in this state are in the 1D KPZ universality class.

中文翻译：

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一维Kardar-Parisi-Zhang和Kuramoto-Sivashinsky普适性类：极限分布

在一维Kardar-Parisi-Zhang（KPZ）随机偏微分方程（PDE）中，Tracy-Widom和Baik-Rains分布作为高度波动的通用极限分布出现。通过进行广泛的拟谱直接数值模拟以获得KS高度剖面的时空演化，我们在一维Kuramoto-Sivashinsky（KS）确定性PDE的时空混沌，非平衡但统计稳定状态下获得相同的通用分布$H（X，Ť）$针对不同的初始条件。因此，我们确定在这种状态下，一维（1D）KS PDE的统计属性属于1D KPZ通用性类。