  We discover the formation of a temporal boundary soliton (TBS) in the close
proximity of a temporal boundary, moving in a nonlinear optical medium, upon
high-intensity pulse collision with the boundary. We show that the TBS
excitation causes giant intensity fluctuations in reflection (transmission)
from (through) the temporal boundary even for very modest input pulse intensity
fluctuations. We advance a statistical theory of the phenomenon and show that
the TBS emerges as an extremely rare event in a nonintegrable nonlinear system,
heralded by colossal intensity fluctuations with unprecedented magnitudes of
the normalized intensity autocorrelation function of the reflected/transmitted
pulse ensemble.
