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The current study is dedicated to the optical soliton solutions and modulation instability of the Cubic–quartic Fokas–Lenells equation with nonlinear perturbation and polarization-preserving fibers. In this direction, we take the help of Lie Symmetry analysis method. First of all, we obtained the invariant condition which plays important role in the mechanism of Lie symmetry method. After that, we developed the appropriate vector fields. Consequently, with the application of these vector fields similarity solutions are obtained in form of trigonometric functions. Further, in this work, optical solitons are obtained for Cubic–quartic Fokas–Lenells equation which are in form of hyperbolic and exponential functions. In addition at the end of this work modulation instability of the Cubic–quartic Fokas–Lenells equation will be discussed.