Dark-soliton collisions for a coupled AB system in the geophysical fluids or nonlinear optics

Under investigation in this paper is a coupled AB system, which describes the marginally unstable baroclinic wave packets in the geophysical fluids or ultra-short pulses in nonlinear optics. As the dark solitons are more resistant against various perturbations than the bright ones, we aim to investigate the dark solitons in the geophysical fluids or nonlinear optics. Dark one- and two-soliton solutions for such a system are derived based on the bilinear forms and propagations of the one solitons and collisions between the two solitons are graphically illustrated and analyzed. Further, influences of the coefficients lambda and sigma on the solitons are discussed, where lambda is a parameter measuring the state of the basic flow and sigma is the group velocity. The dark-one solitons with invariant shapes and amplitudes are viewed, and elastic collisions between the dark-two solitons are observed. Also, elastic collision between the bright and dark solitons is viewed, and the dark soliton is found to possess two peaks. sigma is found to affect the widths of the dark-one solitons and the travelling directions of the dark-two solitons. It is shown that lambda cannot influence shapes of A(1) and A(2), but affect the plane of the one soliton for B, and the two-peak dark soliton for B changes to the single-peak one with the value of lambda decreasing, where A(1) and A(2) are the packets of short waves and B is the mean flow.