标题： 非定常跨音速流中的非线性效应：类黑洞稳定性分析 显示英文标题

标题： Non-linear effects in time-dependent transonic flows: An analysis of analogue black hole stability

摘要： 我们研究一维Gross-Pitaevskii方程的解，以更好地理解流动原子凝聚体中出现的动力学不稳定性。 尽管超音速稳态流动可以用简单的术语完全描述，但时间依赖的流动表现出多种行为。 当声速被穿过一次时，我们观察到类似于黑洞的流动遵循一种"无毛定理"，因为它们的晚期轮廓是稳定的，并且由进入哈密顿量和守恒量的参数唯一确定。 对于类似于白洞的流动，在晚期可以发现超音速侧存在宏观波动，其振幅固定，或者振幅广泛变化，表明在亚音速侧有准周期性的孤子发射。 当考虑两次穿过声速的流动时，我们观察到各种情景，这些情景可以从上述行为以及描述此类流动的动力学不稳定性增长率层次结构中得到理解。 显示英文摘要

摘要： We study solutions of the one dimensional Gross-Pitaevskii equation to better understand dynamical instabilities occurring in flowing atomic condensates. Whereas transonic stationary flows can be fully described in simple terms, time dependent flows exhibit a wide variety of behaviors. When the sound speed is crossed once, we observe that flows analogous to black holes obey a kind of "no-hair theorem" since their late time profile is stationary and uniquely fixed by parameters entering the Hamiltonian and conserved quantities. For flows analogous to white holes, at late time one finds a macroscopic undulation in the supersonic side which has either a fixed amplitude, or a widely varying one signaling a quasi periodic emission of solitons on the subsonic side. When considering flows which cross twice the sound speed, we observe various scenarii which can be understood from the above behaviors, and from the hierarchy of the growth rates of the dynamical instabilities characterizing such flows.