We employ the Gross-Pitaevskii equation to study acoustic emission generated in a uniform Bose gas by a static impurity. The impurity excites a sound-wave packet, which propagates through the gas. We calculate the shape of this wave packet in the limit of long wave lengths, and argue that it is possible to extract properties of the impurity by observing this shape. We illustrate here this possibility for a Bose gas with a trapped impurity atom -- an example of a relevant experimental setup. Presented results are general for all one-dimensional systems described by the nonlinear Schr\"odinger equation and can also be used in nonatomic systems, e.g., to analyze light propagation in nonlinear optical media. Finally, we calculate the shape of the sound-wave packet for a three-dimensional Bose gas assuming a spherically symmetric perturbation.

中文翻译：

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玻色微扰气体中声波的形状

我们使用Gross-Pitaevskii方程研究静态杂质在均匀Bose气体中产生的声发射。杂质激发声波包，该声波包通过气体传播。我们在长波长的极限内计算该波包的形状，并认为可以通过观察这种形状来提取杂质的性质。我们在这里说明了具有被捕获的杂质原子的玻色气体的这种可能性-相关实验装置的一个例子。给出的结果对于由非线性薛定od方程描述的所有一维系统都是通用的，也可用于非原子系统，例如，分析非线性光学介质中的光传播。最后，我们计算声波的形状假设球对称扰动的三维玻色气体的气体包。