Superfluorescence (SF) is studied under the assumption that the pumpin
g and the SF processes were not temporally separated but occur simulta
neously. By use of the linearized theory the initiation of SF by fluct
uations is described, and the connection of the linear regime with sel
f-similar solutions of the nonlinear Maxwell-Bloch equations is studie
d. The evolving self-similar solution is of oscillatory character with
decreasing amplitude for the field but with increasing amplitudes for
inversion and polarization.