Bright-dark soliton, breather and semirational rogue wave solutions for a coupled AB system

Abstract

In this manuscript, we consider a coupled AB system, which describes the baroclinic instability processes in the geophysical flows. Darboux-dressing transformation is used to derive the bright-dark soliton, breather and semirational rogue wave solutions for such a system. We observe that type of the solutions is relate to the spectral parameter $$\lambda $$ , amplitude $$a_{1}$$ and wave number q. Elastic collision between dark or bright solitons, propagations of the bright or dark breathers and rogue waves coexist with two dark or bright solitons are respectively illustrated in figures. The results about those localized wave phenomena are expected to have potential applications.