Interactions of Localized Wave Structures on Periodic Backgrounds for the Coupled Lakshmanan–Porsezian–Daniel Equations in Birefringent Optical Fibers

Nonlinear waves on periodic backgrounds play an important role in physical systems. In this study, nonlinear waves that include solitons, breathers, rogue waves, and semi‐rational solutions on periodic backgrounds for the coupled Lakshmanan‐Porsezian‐Daniel equations are investigated. Moreover, the interactions between different types of nonlinear waves are examined and their dynamic behaviors are studied. In particular, it is observed that bright‐dark rogue waves interact with bright‐dark breathers or solitons on periodic backgrounds, four‐petaled breathers interact with two eye‐shaped breathers on periodic backgrounds, and a four‐petal rogue wave interplays with a rogue wave on periodic backgrounds. Furthermore, it is found that the value of the parameter γ3 affects the weak and strong interactions of these nonlinear waves. These results may be useful in the study of nonlinear wave dynamics in coupled nonlinear wave models. Localized waves on periodic backgrounds are constructed by using the matrix analysis and SU(2) transformation for the coupled Lakshmanan–Porsezian–Daniel equations. Moreover, interactions and dynamic behaviors of these localized waves are shown. The results may be applicable to the relevant experimental investigations in optical fibers, fluid dynamics and other media.