  Interaction properties of complex solitons are studied for the two
U(1)-invariant integrable generalizations of the mKdV equation, given by the
Hirota equation and the Sasa-Satsuma equation, which share the same travelling
wave (single-soliton) solution having a {\em sech} profile characterized by a
constant speed and a constant phase angle. For both equations, nonlinear
interactions where a fast soliton collides with a slow soliton are shown to be
described by 2-soliton solutions that can have three different types of
interaction profiles depending on the speed ratio and the relative phase angle
of the individual solitons. In all cases the shapes and speeds of the solitons
are found to be preserved apart from a shift in position such that their center
of momentum moves at a constant speed. Moreover, for the Hirota equation, the
phase angles of the fast and slow solitons are found to remain unchanged, while
for the Sasa-Satsuma equation, the phase angles are shown to undergo a shift
such that the relative phase between the fast and slow solitons changes sign.
