The paper studies the optical solitons with coupled nonlinear Schrödinger system (CNLSS) that describes the propagation of waves in birefringence polarization-preserving fibers with four-wave mixing effect. The system is discussed with the effects of group velocity dispersion, self-phase and cross-phase modulations. The mechanism that is used to investigate is the extended Fan-sub equation method. It is observed that this system exhibits a collection of rich solitons (single and combined) for different values of parameters. The 3D figures are also plotted to show the physical behavior of obtained solutions under different constraint conditions.