Retrieval of the optical soliton solutions of the perturbed Schrödinger–Hirota equation with generalized anti‐cubic law nonlinearity having the spatio‐temporal dispersion.

In this study, we obtained optical soliton solutions of the perturbed nonlinear Schrödinger–Hirota equation with generalized anti‐cubic law nonlinearity in the presence of spatio‐temporal dispersion. This equation models the propagation of optical pulses in fiber optic cables. Due to the anti‐cubic nonlinearity, perturbation, and spatio‐temporal dispersion present in the model, it provides more accurate results for high‐speed and long‐distance transmissions. Given the significant developments in the field of optics, studies on complex equations such as this model are of great importance. With the increase in real‐life applications, obtaining solutions to optical equations has become crucial. In this study, we used the improved F‐expansion method to derive the optical soliton solutions for the relevant model. This technique allows for obtaining various solutions through the Jacobi elliptic auxiliary functions it employs. The obtained solutions consist of trigonometric and hyperbolic functions. As a result of the application, 10 solutions were obtained, and 2D and 3D graphics of these solutions are included. These graphs illustrate the motion directions of optical solitons and the effect of the nonlinearity parameter p$$ p $$ and spatio‐temporal dispersion parameter β$$ \beta $$ on soliton behavior. No restrictions were encountered during the study. Finally, the originality of the study lies in the first application of this technique to the relevant model and in examining the effect of the parameters p$$ p $$ and β$$ \beta $$ on this model. [ABSTRACT FROM AUTHOR]