Replica Symmetry Breaking in higher-order optical soliton fission

We investigate the statistical properties of higher-order soliton fission resulting from the propagation of partially coherent input pulses, based on numerical solutions of the one-dimensional Nonlinear Schrödinger Equation (NLSE). The findings reveal a frustrating competition for energy among the multiple solitons generated during the fission process, characterized by spin-glass-like correlations and supported by the manifestation of Replica Symmetry Breaking (RSB) in the temporal profile of the propagating pulse. This behavior arises from the interplay between nonlinear (NL) compression and random temporal phase fluctuations, which redistribute energy among the generated solitons while preserving the soliton order parameter. The evolution of the Parisi overlap parameter |qmax| shows a non-monotonic behavior: it gradually decays after successive fissions and re-emerges in a second RSB manifestation, reflecting transitions analogous to those observed in random lasers. These results provide key insights into pulse propagation dynamics in the presence of disorder, and open new avenues for controlling soliton interactions in NL optical systems, with potential applications in photonics and telecommunications.