Shape of a sound wave in a weakly-perturbed Bose gas

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