Coupling dynamics of dissipative localized structures: From polarized vector solitons to soliton molecules

Dissipative solitons are well known as representative nonlinear localized wave packets resulting from the composite balance of dispersion, nonlinearity, gain and loss in optical cavities. Since the last three decades, dissipative solitons keep as one of the most active research topics in the framework of nonlinear physics, not only for fundamental researches but also for various industrial applications. From one hand, due to the rich nonlinear dynamics, dissipative solitons have been considered as an ideal testbed to study the pumping-dissipation-bifurcation complexities. On the other hand, the emergences of dissipative solitons are tightly linked with the emission of ultrashort laser pulses, as well as the formation of broadband optical frequency combs. Compared with single-soliton counterpart, the multi-component dissipative solitons have exhibited even more fascinating properties and much wider range of applications, therefore the coupling dynamics of dissipative solitons is the blooming and emergent research area in the last decade. From this point of view, this review article covers the latest developments of compound dissipative solitons, not only in passive Kerr resonators, but also in mode-locked laser cavities. Ranging from polarized vector solitons to soliton molecules, the rising degree of freedom of these multi-component localized structures is boosting the discovery of novel nonlinear dynamics and underpin the various photonic applications in light science.