Bifurcation dynamics and optical soliton structures in the nonlinear Schrödinger–Bopp–Podolsky system

Abstract In this article, the complex structure of optical soliton solutions of the nonlinear Schrödinger–Bopp–Podolsky system is investigated using the enhanced modified extended tanh-expansion approach. It also analyzes the system’s stability and how it changes by performing a bifurcation analysis. This system holds special importance in nonlinear optics because it describes light-wave behavior when they interact with nonlinear materials. The enhanced modified extended tanh-expansion method serves as a strong analytical method to construct numerous innovative and diverse optical solitons including dark and bright and singular types. The obtained solutions help researchers understand all aspects that influence the nonlinear Schrödinger–Bopp–Podolsky system behavior while providing tools for simulating nonlinear optical processes. The potential for discovering new types of optical soliton solutions specific to the Schrödinger–Bopp–Podolsky system, which may differ from those found in other systems, remains untapped. While the current literature demonstrates the effectiveness of the enhanced modified extended tanh-method in various contexts, its application to the nonlinear Schrödinger–Bopp–Podolsky system could provide new insights and expand the understanding of soliton dynamics in modified nonlinear systems.This study is innovative because it is the first to apply the enhanced modified extended tanh-method to the nonlinear Schrödinger–Bopp–Podolsky system. This approach enables the construction of new soliton solutions and provides a deeper understanding of the nonlinear dynamics of the system. We employed Mathematica and MATLAB together to provide comprehensive, illustrative, and high-quality visualizations of the findings for graphical representation.