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Higher-order matter rogue waves and their deformations in two-component Bose–Einstein condensates

We construct matter rogue wave (RW) solutions for both attractive-attractive and repulsive-repulsive two-component Bose–Einstein condensates (BECs). With the help of similarity transformation, we transform the two coupled Gross–Pitaevskii (GP) equations into Manakov equation with an integrability condition. For attractive-attractive two-component BECs, we obtain various localized patterns, namely first-order dark-bright RW, doublets, triplets, quartets and sextet RWs. We explore the dynamical properties of the obtained RW solutions by considering three distinct forms of trap potentials, namely the time-independent trap, time-dependent monotonic trap and time-dependent periodic trap. Further, we derive first-order dark-bright, dark-dark doublet, dark-bright triplet and dark-dark triplet RW solutions for two-component BECs with repulsive interactions. We then analyze the deformation of these solutions for the same three kinds of trap potentials. Our results show that the robustness of the matter RWs can be manipulated with the help of the trap parameter.