Semi-rational vector rogon–soliton solutions of the five-component Manakov/NLS system with mixed backgrounds

Abstract The five-component Manakov system (alias 5-Manakov system) appears in many fields such as nonlinear optics, Bose–Einstein condensates (alias the spin-2 Gross–Pitaevskii equation), and ocean. In this Letter, we investigate the semi-rational vector rogon–soliton and soliton of the 5-Manakov system with mixed zero and non-zero backgrounds by using the modified Darboux transform. The key point is to explicitly solve the multiple roots of a sixth degree characteristic polynomial equation. In particular, we exhibit the wave structures of the fundamental semi-rational vector rogon with grey solitons and soliton solutions, and their higher-degree forms. Moreover, the semi-rational vector rogon with grey solitons corresponding to the components with non-zero backgrounds are P T -symmetric. These semi-rational wave structures will be useful to further understand some related physical phenomena and to design the relative experiments.