  We study the propagation of ultra-short pulses in a cubic nonlinear medium.
Using multiple-scale technique, we derive a new wave equation that preserves
the nonlocal dispersion present in Maxwell's equations. As a result, we are
able to understand how ultra-short nonlinear shocks are stabilized by
dispersive terms. A delicate balance between dispersion and nonlinearity leads
to a new type of solitary waves. Their stability is confirmed by numerical
simulations of full Maxwell's equations.
