Abstract
In this paper, we investigate a three-component AB model, which characterizes the baroclinic instability processes in the geophysical flows. Via the Darboux transformation, the breather solutions are derived. Then, we study the state transition and find that the breather solutions can be transformed into different kinds of stationary nonlinear waves, including the anti-dark soliton, multi-peak soliton, M-shaped soliton, W-shaped solitons and periodic waves. Moreover, by virtue of the second-order transformed solution, various nonlinear wave complexes are presented. Finally, we unveil the relationship between the modulation instability and state transition and show the existence regions for the transformed waves.
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