  Using the Balitsky-Kovchegov (BK) equation as an explicit example, we show
that nonlinear QCD evolution leads to an instability in the propagation toward
the infrared of the gluon transverse momentum distribution, if one starts with
a state with an infrared cut-off. This effect takes the mathematical form of
rapidly moving traveling wave solutions of the BK equation, which we
investigate by numerical simulations. These traveling wave solutions are
different from those governing the transition to saturation, which propagate
towards the ultraviolet. The infrared wave speed, formally infinite for the
leading order QCD kernel, is determined by higher order corrections. This
mechanism could play a role in the rapid decrease of the mean free path in the
Color Glass Condensate scenario for heavy ion collisions.
