Cubic-quartic optical soliton perturbation and modulation instability analysis in polarization-controlled fibers for Fokas-Lenells equation

The objective of this study is to investigate miscellaneous wave structures for perturbed Fokas-Lenells equation (FLE) with cubic-quartic dispersion in polarization-preserving fibers. Based on the improved projective Riccati equations method, various types of soliton solutions such as bright soliton, combo dark-bright soliton, singular soliton and combo singular soliton are constructed. Additionally, a set of periodic singular waves are also retrieved. The dynamical behaviors of some obtained solutions are depicted to provide a key to understanding the physics of the model. The modulation instability of the FLE is reported by employing the linear stability analysis which shows that all solutions are stable.