Asymptotic behaviors and dynamics of degenerate and mixed solitons for the coupled Hirota system with strong coherent coupling effects

In this work, we investigate the asymptotic behaviors and dynamics of degenerate and mixed solitons in the coupled Hirota system with strong coherent coupling effect. Through the binary Darboux transformation, we obtain three types of degenerate solitons and their asymptotic expressions. These degenerate solitons admit time-dependent velocities, and the relative distance between the two asymptotic solitons logarithmically increases with the increase in the higher-order perturbation parameter |ε|. We also reveal four mechanisms of interaction between degenerate solitons and bell-shaped solitons: (1) elastic interaction with a position shift; (2) inelastic interaction for the degenerate soliton but elastic for the bell-shaped one; (3) elastic interaction for the degenerate soliton but inelastic for the bell-shaped one; and (4) elastic interaction based on coherent interaction under specific parameter conditions. Furthermore, we analyze a special degenerate vector soliton with strong coherent coupling effects, and through numerical studies, we investigate the relationship between the soliton's robustness and the parameter ε. The results show that ε significantly affects the coherence of the solitons, and its robustness decreases as |ε| increases. Our research results not only provide a new theoretical basis for understanding soliton dynamics, but also offer important guidance for practical applications, such as optical fiber communication and fluid dynamics.