  Following our previous work [J. Ieda, T. Miyakawa, M. Wadati,
cond-mat/0404569] on a novel integrable model describing soliton dynamics of an
F=1 spinor Bose--Einstein condensate, we discuss in detail the properties of
the multi-component system with spin-exchange interactions. The exact multiple
bright soliton solutions are obtained for the system where the mean-field
interaction is attractive (c_0 < 0) and the spin-exchange interaction is
ferromagnetic (c_2 < 0). A complete classification of the one-soliton solution
with respect to the spin states and an explicit formula of the two-soliton
solution are presented. For solitons in polar state, there exists a variety of
different shaped solutions including twin peaks. We show that a "singlet pair"
density can be used to distinguish those energetically degenerate solitons. We
also analyze collisional effects between solitons in the same or different spin
state(s) by computing the asymptotic forms of their initial and final states.
The result reveals that it is possible to manipulate the spin dynamics by
controlling the parameters of colliding solitons.
