Dark solitons for a variable-coefficient AB system in the geophysical fluids or nonlinear optics

.Under investigations in this paper is a variable-coefficient AB system, which describes the marginally-unstable baroclinic wave packets in a geophysical fluid or ultra-short pulses in nonlinear optics with certain inhomogeneous medium existing, while the binary Darboux transformation constructed and dark solitons derived. Moreover, effects of the coefficients alpha(t) and beta(t) , which are, respectively, the parameters measuring the state of the basic flow and reflecting the interaction of the wave packet and mean flow under inhomogeneous situations, are discussed in figures. Compared with the constant-coefficient AB system, there may appear some new interesting phenomena in the variable-coefficient one, for example, we find that the variable coefficients cannot only influence the amplitudes of the solitons but the velocities.