Slow and fast modulation instability and envelope soliton of ion-acoustic wave (IAW) are studied in an electron–ion–positron plasma when the ions are warm and have constant stream velocity, positrons are isothermal and electrons are superthermal. The non-linear Schrodinger (NLS) equation has been derived using the Fried and Ichikawa method and the solution of envelope soliton is obtained. It is seen that IAW propagates with two modes (slow and fast) in the presence of an ion stream in the plasma which results in slow and fast modulation instability of the wave. The stability criteria for slow mode (SM) and fast mode (FM) of the wave are established and studied graphically for different values of the ion temperature, positron density, positron temperature and kappa factor of electrons. The bright envelope soliton and dark envelope soliton of SM and FMs of the wave in electron–ion–positron plasma are also studied. The solution of rogue waves (RWs) is obtained from the NLS equation and the nature of RWs of the SM and FM of the wave is discussed graphically. Our results are new and no author has reported this kind of results of slow and fast modulation instability of IAW till now.

在电子-离子-正电子等离子体中，当离子温暖且流速恒定、正电子等温且电子超热时，研究了离子声波 (IAW) 的慢速和快速调制不稳定性和包络孤子。利用Fried和Ichikawa方法推导出非线性薛定谔(NLS)方程，得到包络孤子的解。可以看出，在等离子体中存在离子流的情况下，IAW 以两种模式（慢速和快速）传播，这导致波的慢速和快速调制不稳定性。建立了波的慢模式 (SM) 和快模式 (FM) 的稳定性标准，并针对离子温度、正电子密度、正电子温度和电子 kappa 因子的不同值进行了图形研究。还研究了电子-离子-正电子等离子体中波的SM和FMs的亮包络孤子和暗包络孤子。从 NLS 方程获得流氓波 (RW) 的解，并以图形方式讨论了波的 SM 和 FM 的 RW 性质。我们的结果是新的，到目前为止还没有作者报告过这种 IAW 慢速和快速调制不稳定性的结果。