It is shown that optical pulses in dispersive media with dissipation a
nd saturable broadband gain experience frequency self-shifting toward
the point of zero group-velocity dispersion. The decreasing dispersion
leads to a strong compression of the pulses at constant pulse energy.
The ultrashort pulses that result from this evolution have a duration
limited only by the third-order group-velocity dispersion of the medi
um. A set of solitonlike pulses is found that has a continuous spectru
m of velocities, and a selection rule is presented to determine the un
ique solution established from an arbitrary initial pulse form.