Nonlinear interactions between nonlinearity, dispersion, and other phenomena in a media give rise to solitons, which are self-reinforcing solitary waves that retain shape and velocity as they propagate across the medium. We investigate electrostatic ion-acoustic solitary waves in a homogeneous, un-magnetized, collision-less plasma environment at 200–500 km for a plasma system consists of three positive ions, whereas the electrons present as a super-thermal charges and follow kappa distribution function. The potential for electrostatic ion-acoustic solitary waves to form in the Martian ionosphere due to the movement of different ionic species was established using the one-dimensional Korteweg-de Vries (KdV) equation has been obtained using the reductive perturbation approach. Graphical representations of numerical studies that explain how super-thermal parameter affects nonlinear ion acoustic waves are shown. The kappa index influence on the soliton waves has been studied. Based on our model an increased kappa index can lead to modifications in soliton amplitude and width.