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Figure 1.  BOs under different parameters F, g, and λ for R = 10.

Figure 2.  Phase diagram for maintaining the long-lived BOs in g–λ plane.

Figure 3.  BOs for parameters corresponding to the points (A, B, C, D, E, and F) marked in Fig. 2: (a) λ = 0.5, (b) g = 0.1. The other system parameters are F = 0.1 and R = 10.

Figure 4.  Temporal evolutions of Gaussian wave packet: (a) ω = ω_k = F₀/ν₁ = 0.0832, (b) ω = ω_n = F₀ / π = 0.0637, (c) ω = 0.0450, (d) ω = ω_k = F₀ / ν₂ = 0.0362, (e) ω = ω_n = F₀ / 2π = 0.0318, (f) ω = 0.0250. The other system parameters are p₀ = 0, g = 0.1, λ = 0.5, F₀ = 0.2, and R = 10.

Figure 5.  Temporal evolutions of Gaussian wave packet: (a) ω = ω_k = F₀/ν₁ = 0.0832, (b) ω = ω_n = F₀ / π = 0.0637, (c) ω = 0.0450, (d) ω = ω_k = F₀/ν₂ = 0.0362, (e) ω = ω_n = F₀ / 2π = 0.0318, (f) ω = 0.0250. The other system parameters are p₀ = 0, g = 0.1, λ = −1.15, F₀ = 0.2, and R = 10.

Figure 6.  The same as Fig. 5 but with g = 0 and λ = 0.