Investigation on the behaviors of the soliton solutions for a variable-coefficient generalized AB system in the geophysical flows

Under investigation in this paper is a variable-coefficient generalized AB system, which is used for modeling the baroclinic instability in the asymptotic reduction of certain classes of geophysical flows. Bilinear forms are obtained, and one-, two- and three-soliton solutions are derived via the Hirota bilinear method. Interaction and propagation of the solitons are discussed graphically. Numerical investigation on the stability of the solitons indicates that the solitons could resist the disturbance of small perturbations and propagate steadily.