Rapidly decaying long-period oscillations often occur in hot coronal loops of active regions associated with small (or micro-) flares. This kind of wave activity was first discovered with the SOHO/SUMER spectrometer from Doppler velocity measurements of hot emission lines, thus also often called “SUMER” oscillations. They were mainly interpreted as global (or fundamental mode) standing slow magnetoacoustic waves. In addition, increasing evidence has suggested that the decaying harmonic type of pulsations detected in light curves of solar and stellar flares are likely caused by standing slow-mode waves. The study of slow magnetoacoustic waves in coronal loops has become a topic of particular interest in connection with coronal seismology. We review recent results from SDO/AIA and Hinode/XRT observations that have detected both standing and reflected intensity oscillations in hot flaring loops showing the physical properties (e.g., oscillation periods, decay times, and triggers) in accord with the SUMER oscillations. We also review recent advances in theory and numerical modeling of slow-mode waves focusing on the wave excitation and damping mechanisms. MHD simulations in 1D, 2D and 3D have been dedicated to understanding the physical conditions for the generation of a reflected propagating or a standing wave by impulsive heating. Various damping mechanisms and their analysis methods are summarized. Calculations based on linear theory suggest that the non-ideal MHD effects such as thermal conduction, compressive viscosity, and optically thin radiation may dominate in damping of slow-mode waves in coronal loops of different physical conditions. Finally, an overview is given of several important seismological applications such as determination of transport coefficients and heating function.

快速衰减的长周期振荡通常发生在与小（或微）耀斑相关的活动区域的冠状热圈中。这种波活动首先是通过SOHO / SUMER光谱仪从热辐射线的多普勒速度测量中发现的，因此也常被称为“ SUMER”振荡。它们主要被解释为整体（或基本模式）的慢磁声波。另外，越来越多的证据表明，在太阳耀斑和恒星耀斑的光曲线中检测到的脉动的衰减谐波类型可能是由慢波驻波引起的。对日冕环中慢磁声波的研究已成为与日冕地震学有关的特别感兴趣的话题。我们回顾了SDO / AIA和Hinode / XRT观测的最新结果，这些观测结果已检测到热扩环中的站立和反射强度振荡，显示出与SUMER振荡一致的物理特性（例如，振荡周期，衰减时间和触发）。我们还将回顾慢波的理论和数值建模方面的最新进展，重点放在波浪的激励和阻尼机制上。在1D，2D和3D中进行MHD仿真已专门用于理解物理条件，以便通过脉冲加热产生反射的传播波或驻波。总结了各种阻尼机理及其分析方法。根据线性理论进行的计算表明，非理想的MHD效应（例如热传导，压缩粘度，光学上薄的辐射可能在不同物理条件的日冕环中的慢模波的衰减中起主要作用。最后，概述了几个重要的地震应用，例如传输系数和加热函数的确定。