We investigate the propagation of acoustic singular surfaces, specifically, linear shock waves and nonlinear acceleration waves, in a class of inhomogeneous gases whose ambient mass density varies exponentially. Employing the mathematical tools of singular surface theory, we first determine the evolution of both the jump amplitudes and the locations/velocities of their associated wave-fronts, along with a variety of related analytical results. We then turn to what have become known as Krylov subspace spectral (KSS) methods to numerically simulate the evolution of the full waveforms under consideration. These are not only performed quite efficiently, since KSS allows the use of `large' CFL numbers, but also quite accurately, in the sense of capturing theoretically-predicted features of the solution profiles more faithfully than other time-stepping methods, since KSS customizes the computation of the components of the solution corresponding to the different frequencies involved. The presentation concludes with a listing of possible, acoustics-related, follow-on studies.

翻译：我们研究了一类背景质量密度呈指数变化的非均匀气体中声学奇异面的传播，具体包括线性激波和非线性加速波。利用奇异面理论的数学工具，我们首先确定了跳跃振幅及其相关波前的位置/速度的演化，以及一系列相关的解析结果。随后，我们转向Krylov子空间谱（KSS）方法，以数值模拟所考虑完整波形的演化。由于KSS允许使用“大”CFL数，这些模拟不仅执行得相当高效，而且相当精确——在捕捉理论上预测的解剖面特征方面比其他时间步进方法更忠实，因为KSS针对所涉及的不同频率定制了求解分量的计算。本文最后列出了可能的声学相关后续研究方向。