The existence of both subsonic \((M < 1)\) and supersonic \((M > 1)\) compressive \((N > 1)\) solitons within a three-dimensional magnetized plasma model featuring thermal ions and electrons, incorporating electron inertia through the pseudopotential method is established. The study delves into ion-acoustic solitary waves, numerically exploring the dependency of the solitary wave profile on different plasma parameters. The findings suggest that, as the ion temperature \((\alpha )\) increases, both subsonic and supersonic potential profiles exhibit a decrease in amplitude and depth. Furthermore, the study investigates the influence of the Mach number on the potential profile. It reveals that as the Mach number increases in the direction of wave propagation, the amplitude and depth of the potential profile also increase. The findings not only enrich our understanding of the intricate dynamics of plasmas but also provide profound insights with broad applicability, encompassing natural and engineered plasma systems across diverse scientific and technological domains.
