This paper investigates the self-action effects of two co propagating \(q\) -Gaussian laser beams within a Kerr nonlinear medium under the influence of electromagnetically induced transparency (EIT). The interplay between the spatial profile of the \(q\) -Gaussian beams and the nonlinear optical properties of the medium is explored, focusing on their mutual self-focusing, self-defocusing, and cross-phase modulation dynamics. By leveraging EIT, we achieve an effective enhancement of nonlinear interactions while suppressing absorption, enabling the propagation of “slow light” with minimal distortion. The study demonstrates that the beam parameters, such as the \(q\) -factor and intensity ratio, strongly influence the beam coupling and the induced nonlinear refractive index changes. Furthermore, we analyze how these self-action effects modify the group velocity of the slow light in the medium, revealing novel opportunities for controlling light propagation in nonlinear and quantum optical systems. The results provide insights into advancing applications in optical information processing, nonlinear beam shaping, and slow-light-based technologies.
