  A theory of an optical vector pulsing soliton of self-induced transparency in
an ensemble of semiconductor quantum dots is investigated. It is shown that a
distribution of the excitonic ground-state transition dipole moments of the
quantum dots and phase modulation changes significantly the pulse parameters.
The profile of a circularly polarized optical two-component vector pulsing
soliton with the difference and sum of the frequencies in the region of the
carrier frequency is presented. It is shown that the vector pulsing soliton in
the special case can be reduced to the scalar breather solution and these
nonlinear waves have different shapes. Explicit analytical expressions for the
optical vector pulsing soliton are obtained with realistic parameters which can
be reached in current experiments.
