Periodic attraction and repulsion within the tight-bound π-phase soliton molecule

In the over-pumped dissipative system, the single pulse is prone to split into multi-soliton modes, among which the soliton molecule (SM) comprising two pulses has attracted much interest recently. In this Letter, the tight-bound SM with the π-phase-difference, a soliton pair predicted to be unstable observed in fiber lasers, is found to have oscillating separation with excellent stability. For the first time, to the best of our knowledge, we reveal the mechanism of the π-phase SM to circumvent the irreversible repulsion and the role of dispersive waves on the SM. During the periodic propagation, the destructive interference between solitons produces the repulsion while the dispersive waves give rise to the attractive force, leading to the dynamic oscillating behavior of the SM. The numerical simulation reproduces the experimental observation and offers panoramic insights into the nonlinear interactions between multiple components in dissipative systems.