Numerical Validation of Certain Cubic–Quartic Optical Structures Associated with the Class of Nonlinear Schrödinger Equation

This study presents a comprehensive investigation of cubic–quartic solitons within birefringent optical fibers, focusing on the effects of the Kerr law on the refractive index. The researchers have derived soliton solutions analytically using the sine-Gordon function technique. To validate their analytical results, the study employs the improved Adomian decomposition method, a numerical technique known for its efficiency and accuracy in solving nonlinear problems. This method effectively approximates solutions while minimizing computational errors, allowing for reliable numerical simulations that corroborate the analytical findings. The insights gained from this research contribute to a deeper understanding of the symmetry properties involved in nonlinear wave propagation in optical fibers. The study highlights the significant role of nonlinearities in shaping the behavior of waves within these systems. The use of proposed method not only serves as a checking mechanism for the sine-Gordon solutions but also illustrates its potential applicability to other nonlinear systems exhibiting complex symmetry behaviors. This versatility could lead to new exploration fronts in nonlinear optics and photonics, expanding the toolkit available for researchers in these rapidly evolving fields.