Fig. 1. The density distributions |Ψ_{± 1,0}|² and phase diagrams at t = 0 of the vortex solution (9) of the rotating spin-1 BECs for topological charge α = 1. (a1)–(a4) Evolution of the density distributions |Ψ₁(x,y,0)|² for different radial quantum numbers n and the phase diagram. (b1)–(b4) Evolution of the density distributions |Ψ_–1(x,y,0)|² for different radial quantum numbers n and the phase diagram. (c1)–(c4) Evolution of the density distributions |Ψ₀(x,y,0)|² for different radial quantum numbers n and the phase diagram. The parameters are taken as Ω = 0.5, μ₁ = 8, μ₂ = 4, ϵ = 0 and Ω₀ = 1.

Fig. 2. The density profiles |Ψ_{± 1,0}|² and phase diagrams at t = 0 for the vortex solution (9) of the rotating spin-1 BECs for different topological charge α and fixed quantum number n = 1. The blue lines denote the density profiles |Ψ_{± 1,0}|² for the topological charge α = 1, respectively. The green lines denote the density profiles |Ψ_{± 1,0}|² for the topological charge α = 2 and the red lines denote the density profiles |Ψ_{± 1,0}|² for the topological charge α = 3, respectively.

Fig. 3. The evolution of density distributions |ψ_{± 1,0}|² and phase diagrams for the vortex solution (9) of the rotating spin-1 BECs for different values of topological charge α and fixed quantum number n = 1. The first column is stable vortex for the topological charge α = 1. The second and third columns are unstable vortex for the topological charge α = 2 and α = 3, respectively. The parameters are Ω = 0.5, μ₁ = 8, μ₂ = 4, ϵ = 0 and ω₀ = 1. The domain is (x,y) ∈ [–5,5] × [–5,5] for all the cases.

Fig. 4. The evolution of density distributions |ψ_{± 1,0}|² and phase diagrams for the vortex solution (9) of the rotating spin-1 BECs for the fixed topological charge α and different quantum number n = 1. (a1)–(c3) Evolution of density distributions |ψ_{± 1,0}|² and phase diagrams for the quantum number n = 1. (d1)–(f3) Evolution of density distributions |ψ_{± 1,0}|² and phase diagrams for the quantum number n = 2. The parameters are Ω = 0.5, μ₁ = 8, μ₂ = 4, ϵ = 0 and ω₀ = 1.

Fig. 5. Time evolution of density distributions |ψ_{± 1,0}|² and phase diagrams for the vortex solution (9) of the rotating spin-1 BECs for different values of topological charge α and quantum number n. The first three lines show the evolution of density distributions |ψ_{± 1,0}|² and phase diagrams for n = α = 1. The three lines in the middle show the evolution of density distributions |ψ_{± 1,0}|² and phase diagrams for n = 1 and α = 2. The last three lines demonstrate the evolution of density distributions |ψ_{± 1,0}|² and phase diagrams for n = 2 and α = 1. The parameters are Ω = 0.5, μ₁ = 8, μ₂ = 4, ϵ = 0.1 and ω₀ = 0.2.