This study is motivated by recent observations from the Parker Solar Probe (PSP) mission, which have been identified as ion-acoustic waves from 15 to 25 solar radii. These observations reveal characteristic sequences of narrowband, high-frequency bursts exceeding 100 Hz embedded into a slower evolution around 1 Hz, persisting for several hours. To explore the potential role of the ion-acoustic instability (IAI) in these phenomena, we begin by reviewing classical findings on the IAI within the framework of linear kinetic theory. Focusing on proton distributions comprising both a core and a beam component, we analyze the IAI instability range and growth rates within the parameter regime relevant to PSP observations. Our findings indicate that the IAI can indeed occur in this regime, albeit requiring electron-to-core and beam-to-core temperature ratios slightly different from reported values during electrostatic burst detection. Furthermore, employing one-dimensional kinetic plasma simulations, we validate the growth rates predicted by linear theory and observe the saturation behavior of the instability. The resultant nonlinear structures exhibit trapped proton beam populations and oscillatory signatures comparable to those observed, both in terms of timescales and amplitude.