  Self-similar propagation of ultrashort, parabolic pulses in a laser resonator
is observed theoretically and experimentally. This constitutes a new type of
pulse-shaping in modelocked lasers: in contrast to the well-known static
(soliton-like) and breathing (dispersion-managed soliton) pulse evolutions,
asymptotic solutions to the nonlinear wave equation that governs pulse
propagation in most of the laser cavity are observed. Stable self-similar
pulses exist with energies much greater than can be tolerated in soliton-like
pulse shaping, and this will have implications for practical lasers.
