Fig. 1. Density distribution of the condensate at initial time (λ01=2.0). (a) Atom interaction increases exponentially with time (A=0.02); (b) atom interaction decreases exponentially with time (A=-0.02)

Fig. 2. Trajectories of bright soliton at λ01=2.0

Fig. 3. Reflection behavior of solitons in condensates with unchanged atom interaction when v=0.42400, g=-2.0, x0=-12.0, and ω=0.1

Fig. 4. Transmission behavior of solitons in condensates with unchanged atom interaction when v=0.42500, g=-2.0, x0=-12.0, and ω=0.1

Fig. 5. Localization behavior of solitons in condensates with unchanged atom interaction when v=0.42474, g=-2.0, x0=-12.0, and ω=0.1

Fig. 6. Critical local speed of solitons in condensates with unchanged atom interaction varying with potential frequency when g=-2.0 and x0=-12.0

Fig. 7. Change of soliton position under different atom interactions when vc=0.42474, x0=-12.0, and ω=0.1

Fig. 8. Reflection-transmission transition of solitons in condensates when v=0.42473, x0=-12.0, and ω=0.1

Fig. 9. Transmission-reflection transition of solitons in condensates when v=0.42476, x0=-12.0, and ω=0.1

Fig. 10. Localization behavior of solitons in inhomogeneous condensates when v=0.39777, k=0.001, x0=-12.0, and ω=0.1

Fig. 11. Critical local speed of solitons in inhomogeneous condensates varying with the potential frequency when k=0.001 and x0=-12.0

Fig. 12. Periodic oscillation behavior of solitons in condensates when v=0, k=0.001, x0=-12.0, and ω=0.02

Fig. 13. Oscillation period of solitons under different interatomic interactions when v=0, x0=-12.0, and ω=0.02

Fig. 14. Oscillation period of solitons at different potential frequencies when v=0, x0=-12.0, and k=0.001