<p>This paper employs the new Kudryashov method, noted for its ease of application to complex equations and computational efficiency, to obtain solutions for the perturbed Schrödinger–Hirota equation with Kudryashov’s law and spatio-temporal dispersion. After deriving the solutions, we perform a graphical analysis to investigate how key parameters affect soliton dynamics. Kudryashov’s law provides an effective framework for modeling nonlinear terms, offering a refined description of soliton behavior and wave propagation in optical fibers. We visualize the analytical solutions using three-dimensional, contour, and two-dimensional plots, which highlight the characteristics of bright, dark, and W-shaped solitons and illustrate the effects of key parameters on their behavior. The findings offer valuable insights into optimizing next-generation optical technologies and contribute to broader fields such as nonlinear optics and photonics.</p>