This paper investigates the dynamics and existence of ion acoustic (IA) solitary waves propagating obliquely in a three dimensional magnetized plasma model, consisting of hot inertial ions and inertialess electrons obeying Tsallis \(q\) -nonextensive distribution. By applying the Sagdeev pseudopotential approach, the characteristic features and formation of arbitrary amplitude IA waves in such a plasma model have been addressed, taking into account the combined effect of finite ion temperature and electron nonextensivity. The parametric regime in which nonlinear structures occur has been determined, and it has been seen that both subsonic and supersonic Mach number regimes exist. Moreover, the Sagdeev potential and the solitary wave profile are examined analytically and numerically with different plasma configurations and the conditions for the formation of the IA solitary waves and their basic properties are studied in details. It reveals that the plasma model under consideration facilitates both compressive and rarefactive IA solitary structures, and that the insertion of ion temperature effect significantly alter the dynamical properties of IA solitary waves as well as the parametric domain of their existence. The results of the present study should clarify to understand the nonlinear electrostatic localized wave structures that spread in cosmic and astrophysical plasma situations where the effects of magnetic field and nonextensivity can have vital roles.
