The main aim of the presented paper is to obtain the exact solutions of the generalized Sasa–Satsuma equation using two different methods, the modified auxiliary equation method and \((\frac{G'}{G},\frac{1}{G})\) -expansion method. As a result of these methods, new soliton solutions of the given model are extracted. These solutions include rational solutions, hyperbolic solutions and periodic solutions. The necessary constraint conditions for the existence and validity of the constructed solutions are also been provided. Moreover, for appropriate parametric values, acquired findings are displayed via contour, 2D and 3D graphics that show the physical relevance and dynamical behaviors of the proposed equation. The dynamics of constructed solutions of the proposed methods help a lot in describing the propagation of the femtosecond pulses in the systems of optical fiber transmission.
