The propagation of electrostatic ion acoustic waves (IAWs) in a homogeneous, unmagnetized, and collisionless plasma system composed of two positive ions and superthermally distributed electrons is investigated. The three dimensional Kadomtsev-Petviashvili (KP) equation has been derived using the reductive perturbation analysis to describe the dynamics of the weakly nonlinear behavior of electrostatic IAWs in the Venusian ionosphere near the terminator region. A symbolic computational Painlevé analysis is employed to get various solutions of the KP equation. The stability of the localized structures solution against the variation in the transverse direction has been discussed. The condition for the localized pulses existence in the presence of transverse perturbations is examined via the pseudo-potential approach. Numerical studies to elaborate on the physical plasma parameters’ effects on the structural characteristics of nonlinear cnoidal, periodic, and soliton waves are graphically displayed. The model predicts a compressive supersonic IAWs can propagate in the Venusian ionosphere in agreement with the observations.