Bright-dark soliton solutions to the multi-component AB system

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.