Analytical and graphical exploration of optical solitons in birefringent fibers for CNLSEs using modified extended direct algebraic scheme

With the use of the modified extended direct algebraic scheme (MEDAS), this work investigates all possible envelope solitons and their propagation properties in a birefringent fiber where light propagation is controlled by two coupled nonlinear Schrödinger equations (CNLSEs) via coherent and incoherent nonlinear couplings. With regard to elliptical core optical fibers, we investigate the physical significance of different optical solitons in the presence of third-order nonlinearity and group-velocity dispersion. This suggests that a birefringent fiber medium may produce a potentially plentiful array of nonlinear periodic waves and localized pulses. The study’s conclusions have significant implications for the propagation of solitons in nonlinear optics. Possible formulations for the resultant solutions include single periodic solutions, Weierstrass elliptic doubly periodic solutions, singular, dark, and bright solitons, exponential solutions, and Jacobi elliptic functions (JEFs). The wave solutions we found are contrasted with existing literature to illustrate their originality and significant contribution to contemporary study. Given the numerous applications of the studied model, the efficacy of our approach implies that it might be used to a wide variety of nonlinear problems in a broad range of areas, including soliton theory. To further visualize their behaviors, we also displayed the contours of a few of these solutions in 2D and 3D contour plots.