The dynamics of sound in a fluid is intrinsically nonlinear. We derive the consequences of this fact for the analogue gravitational field experienced by sound waves, by first describing generally how the nonlinearity of the equation for phase fluctuations back-reacts on the definition of the background providing the effective space-time metric. Subsequently, we use the analytical tool of Riemann invariants in one-dimensional motion to derive source terms of the effective gravitational field stemming from nonlinearity. Finally, we show that the consequences of nonlinearity we derive can be observed with Bose–Einstein condensates in the ultracold gas laboratory.

中文翻译：

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来自非线性流体动力学的模拟引力场

流体中的声音动力学本质上是非线性的。我们推导出这一事实对声波所经历的模拟引力场的影响，首先一般描述相位波动方程的非线性如何反作用于提供有效时空度量的背景定义。随后，我们利用一维运动中的黎曼不变量分析工具推导了源自非线性的有效引力场的源项。最后，我们表明我们推导的非线性结果可以在超冷气体实验室中用玻色-爱因斯坦凝聚体观察到。