Muniyappan, AnnamalaiSharmila, MuthuvelPriya, Elumalai KaviyaSumithra, SekarBiswas, AnjanYıldırım, YakupAphane, MaggieMoshokoa, Seithuti P.Alshehri, Hashim M.2025-04-092025-04-092022-10-031736-6046 (P)1736-7530 (E)https://doi.org/10.3176/proc.2023.2.04https://hdl.handle.net/20.500.14519/1575Proceedings of the Estonian Academy of SciencesProceedings of the Estonian Academy of SciencesIn the present investigation, we employed the Jacobi elliptic function (JEF) method to invoke the perturbed nonlinear Schr¨odinger equation with self-steepening (SS), self-phase modulation (SPM), and group velocity dispersion (GVD), which govern the propagation of solitonic pulses in optical fibres. The proposed algorithm proves the existence of the family of solitons in optical fibers. Consequently, chirped and chirp free W-shaped bright, dark soliton solutions are obtained from dn(!), cn(!) and sn(!) functions. The final results are displayed in three-dimensional plots with specific physical values of GVD, SPM and SS for an optical fiber.128–144 PagesenAttribution-NonCommercial-ShareAlike 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-sa/4.0/SolitonsJacobi elliptic function methodNLS equationDifferential equationPresentation