We demonstrate that fluid mechanical systems arising from large fluctuations of one-dimensional statistical processes generically exhibit solitons and nonlinear waves. We derive the explicit form of these solutions and examine their properties for the specific cases of the Kipnis-Marchioro-Presutti model (KMP) and the symmetric exclusion process (SEP). We show that the two fluid systems are related by a nonlinear transformation but still have markedly different properties. In particular, the KMP fluid has a nontrivial sound wave spectrum exhibiting birefringence, whereas sound waves for the SEP fluid are essentially trivial. The appearance of sound waves and soliton configurations in the KMP model is related to the onset of instabilities.

中文翻译：

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扩散过程中流体动力学波动的孤子

我们证明，由一维统计过程的大波动引起的流体力学系统通常表现出孤子和非线性波。我们得出这些解决方案的显式形式，并针对Kipnis-Marchioro-Presutti模型（KMP）和对称排除过程（SEP）的特定情况检查其性质。我们表明，两个流体系统通过非线性变换相关，但仍具有明显不同的属性。特别地，KMP流体具有表现出双折射的非平凡的声波谱，而用于SEP流体的声波实质上是平凡的。KMP模型中声波和孤子配置的出现与不稳定性的发生有关。