Bright–dark soliton solutions of the multi-component AB system.

Abstract In this paper, we investigate a multi-component AB system that appears in geophysical fluid dynamics. We construct bright–dark soliton solutions of the system using the Hirota's bilinear method. We obtain asymptotic behaviors of two-soliton solution for the two-component AB system and prove that the interactions between two bright and two dark solitons are elastic. Under various parameter conditions, the oblique interactions and bound states of solitons are analyzed in detail. By use of the Pfaffian technique, we present N -bright and N − dark soliton solutions of the two- and multi-component AB system. The results obtained in this paper can be helpful for the study of vector multi-dark solitons in many physical systems such as nonlinear optics and fluid dynamics. Highlights • We give the bright-and dark-soliton solutions to the two-component AB system. • Dynamics and asymptotic behaviors of two-soliton solutions are presented to show the elastic interactions. • Bound states of solitons are discussed with the explicit periods. • N -bright–dark-soliton solutions are expressed in the compact form by Pfaffian technique. [ABSTRACT FROM AUTHOR]