The optical solitons for the three-component Dirac–Manakov system via the Darboux transformation

The optical solitons represent a fascinating intersection of nonlinear physics and optical technology. In this study, we examine the three-component Dirac–Manakov system through the application of a unified Darboux transformation. We elaborate on the construction of the n-fold Darboux transformation and elucidate the correlation between optical solitons and seed solutions. Our research successfully yields both single-soliton and double-soliton solutions derived from zero-seed solutions. Additionally, we derive periodic solutions from non-zero seed solutions. To visualize these solutions, we employ Maple to generate three-dimensional and density diagrams, thereby facilitating a comprehensive understanding of the solution structures within the three-component Dirac–Manakov system.