  In this paper we investigate the multi-component AB system that comes from
the geophysical fluid dynamics. We construct bright-dark soliton solutions
through Hirota's bilinear method. For the two-component AB system, asymptotic
behaviours of two-soliton solution are obtained and interactions between two
bright and two dark solitons are proved to be elastic. Under different
parameter conditions, the oblique interactions, bound states of solitons are
analyzed in details. Meanwhile, by use of the Pfaffian technique, we present
$N$-bright and $N-$dark soliton solutions to the two- and multi-component AB
system. The results will be meaningful for the study of vector multi-dark
solitons in many physical systems such as nonlinear optics and fluid dynamics.
