Mixed solutions for an AB system in geophysical fluids or nonlinear optics

Abstract

To reveal and analyze the dynamics of degenerate solitons, breathers and mixed breather-rogue waves, we consider an AB system in this manuscript, which models the marginally unstable baroclinic wave packets in geophysical fluids or ultra-short pulses in nonlinear optics. Based on the generalized Darboux transformation, we construct the degenerate soliton, breather and mixed solutions, then some figures are exhibited to illustrate the collision features clearly and some interesting phenomena are shown: (a) Elastic collisions between two solitons with equal amplitude are observed; (b) Collisions between two breathers are plotted, and maximum values of the two breathers keep invariant; (c) Mixture of breather and rogue waves is illustrated. The above wave phenomena are expected to be experimentally observed and have potential applications.