## 5 Discussion on Generation and Stability of Various Soliton Molecules
### Interaction Mechanisms  
As a particular existing form in ultrafast fibre lasers, soliton molecules result from nonlinear interactions between individual solitons via different parameters of the systems. Similar to the ideas in open systems [3; 74] experiencing bidirectional energy exchange with the environment, the dissipative solitons in the dissipative systems of fibre lasers are governed by several effects, namely, dispersion, nonlinearity, gain and loss. In most cases, these effects influence the properties of both single solitons and soliton-soliton interaction in a comprehensive and interdependent fashion, meaning that one cannot simply extract sole impacts from individual terms. One vital example is the relationship between gain and nonlinearity: on the one hand, nonlinearity contains not only the nonlinear Kerr effect from passive fibres but also gain saturation effect from active fibre; on the other hand, since nonlinear Kerr effect is automatically more pronounced with higher gain, variation of gain in experiment leads to variation of nonlinearity. Additionally, it has been reported that the dispersion sign of the gain medium contributes to the stability of soliton molecules [75], indicating that gain and dispersive effects might also be coupled. Similarly, XPM effects can lead to both repulsion and attraction depending on the sign of second-order dispersion. Higher-order dispersion and nonlinearity render pulse-pulse interactions even more complicated. Although the above-mentioned terms are discussed the most frequently and indeed dominate among abundant fibre laser cavities, anisotropy of the fibre cavity is an additional important parameter to influence bound states. In theory, bound states do exist in scalar framework of dissipative systems. In experiment, however, adjustment of the polarization controllers is usually needed to achieve stable bound solitons, which indicates that the role of birefringence cannot be neglected. Very interestingly, when linear and circular birefringence as well as polarization hole burning effects are taken into account, vector soliton molecules with intriguing polarization dynamics can be observed [29]. Group-velocity-locked vector soliton molecules in a birefringence-enhanced fibre laser have also been experimentally evidenced very recently [76]. Moreover, we want to emphasize the key role of historical status in characteristic properties of bound solitons, a common rule in dissipative systems containing discrete attractors. The initial noise or the initial multipulse state triggers how it will evolve and what is the destination state. In another way, time-dependent response functions by for instance slow saturable absorber and gain recovery connect the original state and the ultimate state as well. To give a general idea, the sophisticated interactions mediated by different factors are sketched in Figure 22. All these effects (marked by coloured arrows) play key roles in the dissipative optical process, which contribute to an exact balance of all interaction forces and give rise to an equilibrium status of multiple solitons. The properties of individual solitons as well as the characteristic parameters between solitons are determined by the integrated interplay of all effects. In Figure 22, we use a simple mechanical analogy to mimic this optical system, in which two identical balls are equivalent to the identical solitons and the complicated interactions via different factors behave like a spring to enable the two solitons to feel each other. Despite of the complexity of the interplay, it is rather instructive to analyse the interaction process at different length scales. Depending on the spatial relationship of multiple pulses, short- or long-range physical mechanisms can dominate in the interactions respectively (several examples are listed in Figure 22). When the neighbouring pulses are close to each other, direct and strong soliton-soliton interaction takes place. In this region, [PERSON] et al.