We study theoretically the phenomenon of self-induced transparency for ultrashort pulses (videopulses) propagating in a multilevel quantum medium under conditions in which the method of slowly varying amplitudes and phases breaks down and the pulse spectrum substantially overlaps the quantum transitions. A special class of transitions with one common level is considered. We find that the dynamics of the videopulses in such a medium is described by a double sine-Gordon equation. We establish the conditions under which steady-state traveling 0π-, 2π-, and 4π-videosolitons are formed. It is found that 4π-videosolitons can propagate both in equilibrium media and in some nonequilibrium media while 0π-videosolitons can propagate only in nonequilibrium media. We study amplification processes in highly nonequilibrium systems and show that, depending on the initial state of the medium, 2π- and qπ-pulses (0 < q < 1) with increasing amplitudes may be formed. We conclude that the amplification of an ultrashort pulse occurs due to an increases in the photon number density and to an increase in the frequency of each photon. Finally, we study the possibility of an electromagnetic autosoliton being formed in a nonequilibrium dissipative medium.
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