Shedding and interaction of solitons in imperfect medium

The propagation of a soliton pattern through one-dimensional medium with weakly disordered dispersion is considered. Solitons, perturbed by this disorder, radiate. The emergence of a long-range interaction between the solitons, mediated by the radiation, is reported. Basic soliton patterns are analyzed. The interaction is triple and is extremely sensitive to the phase mismatch and relative spatial separations within the pattern. The phenomenon is a generic feature of any problem explaining adiabatic evolution of solitons through a medium with frozen disorder.