Investigating the generalized Kudryashov’s equation in magneto-optic waveguide through the use of a couple integration techniques

This study addresses the modeling pulse propagation in optical fibers, focusing on a coupled system of nonlinear Schrödinger’s equation for the generalized Kudryashov’s equation in a magneto-optic waveguide. A magneto-optic waveguide is a waveguide that uses the magneto-optic phenomenon to manipulate the movement of light. This phenomenon entails the interplay between a magnetic field and light, which can alter the polarization or orientation of the light wave. Magneto-optic waveguides are frequently utilized in optical communication and computer applications due to their ability to manipulate and regulate light compactly and effectively. In this study, an innovative approach is used to investigate the governing model. By combining the generalized \(\phi ^{6}\) ${\varphi }^6$ -model expansion technique with the enhanced Kudryashov scheme, the study aims to retrieve optical solitons and offer novel solutions for pulse propagation in optical fibers. The application of these methods led to several key findings, including the successful retrieval of bright, dark, and isolated solitons using the enhanced Kudryashov technique. Solutions were obtained through the extended \(\phi ^{6}\) ${\varphi }^6$ -model expansion method, showcased via Jacobi elliptic functions, and additional straddled soliton solutions were also derived. The novelty of this work lies in its unique combination of the generalized \(\phi ^{6}\) ${\varphi }^6$ -model expansion technique and the enhanced Kudryashov scheme, providing fresh insights and extending previous efforts in the literature on optical soliton research. This study goes beyond previous efforts by offering a more comprehensive method for analyzing and understanding pulse propagation in magneto-optic waveguides, marking a significant advancement in the field. The study concludes that the integration technique is brief, straightforward, effective, and versatile enough to be applied to other nonlinear phenomena. This is further supported by a comprehensive discussion section, which enhances understanding through graphical presentations, including three-dimensional (3D) and two-dimensional (2D) plots of the solitons’ structures.