Formation, propagation, and excitation of matter solitons and rogue waves in chiral BECs with a current nonlinearity trapped in external potentials

In this paper, we investigate formation and propagation of matter solitons and rogue waves (RWs) in chiral Bose–Einstein condensates modulated by different external potentials, modeled by the chiral Gross–Pitaevskii (GP) equation with the current nonlinearity and external potentials. On the one hand, the introduction of two potentials (Pöschl–Teller and harmonic-Gaussian potentials) enables the discovery of exact soliton solutions in both focusing and defocusing cases. We analyze the interplay effects of current nonlinearity and potential on soliton stability via associated Bogoliubov–de Gennes equations. Moreover, multiple families of numerical solitons (ground-state and dipole modes) trapped in potentials are found, exhibiting distinctive structures. The interactions between solitons trapped in potentials are studied, which exhibit the inelastic trajectories and repulsive interactions. On the other hand, we introduce the time-dependent potentials such that the controlled RWs are found in both focusing and defocusing GP equations with current nonlinearity. Furthermore, through the interaction between potentials and current nonlinearity, it is possible to enlarge the region of modulational instability, leading to the generation of RWs and chiral solitons. High-order RWs are generated from several Gaussian perturbations on a continuous wave. The presence of current nonlinearity disrupts the structures of these high-order RWs, causing them to undergo a transform into chiral lower-amplitude solitons. Finally, various types of soliton excitations are investigated by varying the strengths of potential and current nonlinearity, showing the abundant dynamic transforms of chrital matter solitons.