In this study, we investigated Schrödinger–Hirota equation Kerr law in the presence of spatio-temporal dispersion which describes pulse propagation in optical fibers provoked by nonlinear effect and reduced to multi-plane dispersion. We used the Lie symmetry method to reduce the model into the nonlinear ordinary differential equations. Moreover, the unified Riccati equation expansion method was used to obtain optical soliton solutions and other soliton solutions of the model. We obtained dark, kink, singular, and periodic-singular soliton solutions. Obtained results were shown via 3D and contour graphs. Thus, the model was analyzed for the first time with the Lie symmetry method and UREEM.