W-shaped profile and breather-like soliton of the fractional nonlinear Schrödinger equation describing the polarization mode in optical fibers

We use the fractional nonlinear Schrödinger equation (FNLSE) to describe polarization mode in optical fiber with Self-Steepening, Self-Frequency Shift, and Cubic-quintic terms analyze effects of time parameter (FTP) on bright dark solitons as well breather-like solitons. transformation hypothesis auxiliary equations method obtain three families solutions such combined soliton, solitons, rational have shown (FP) W-shaped profile, soliton corresponding chirp component. It is observed that for small values FP, shape affected unstable. Moreover, one observes fraction Modulation Instability (MI) gain spectra MI bands. For certain it formed sides lobes specific both stability zone increases amplitude increase while zones increase. To confirm robustness analytical results, we used a numerical investigation. One exhibits formation breathers-like stable FTP. results from this study FP efficient can be an energy source where or are involved communication fibers.