  We obtain explicit bright one- and two-soliton solutions of the integrable
case of the coherently coupled nonlinear Schr{\"o}dinger equations by applying
a non-standard form of the Hirota's direct method. We find that the system
admits both degenerate and non-degenerate solitons in which the latter can take
single hump, double hump, and flat-top profiles. Our study on the collision
dynamics of solitons in the integrable case shows that the collision among
degenerate solitons and also the collision of non-degenerate solitons are
always standard elastic collisions. But the collision of a degenerate soliton
with a non-degenerate soliton induces switching in the latter leaving the
former unaffected after collision, thereby showing a different mechanism from
that of the Manakov system.
