  In this paper, the generalized Darboux transformation is established to the
AB system, which mainly describes marginally unstable baroclinic wave packets
in geophysical fluids and ultra-short pulses in nonlinear optics. We find a
unified formula of Nth-order rogue wave solution for the AB system by the
direct iterative rule. In particular, rogue waves possessing several free
parameters from first to second order are calculated. The dynamics and some
interesting structures of the rogue waves are illustrated through some figures.
