Self-similar interaction of slowly oscillating dispersion-managed solitons

We present an investigation of the interaction of solitons in dispersion-managed fibers beyond the regime of formation of stable pairs (soliton molecules). There is a nonlinear resonance between a slow (compared to the dispersion map period) oscillation of the pulse shape and the typical distance of bouncing of the pulses off each other. Parameter ranges for either repetitive bouncing or a final split of the pair are shown to be organized in a self-similar pattern. Predictions of a theoretical model agree well with numerical simulations.