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Exact wave solutions for Bose–Einstein condensates with time-dependent scattering length and spatiotemporal complicated potential
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10.1063/1.4803458
/content/aip/journal/jmp/54/5/10.1063/1.4803458
http://aip.metastore.ingenta.com/content/aip/journal/jmp/54/5/10.1063/1.4803458
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The dynamics of a solitary wave in a modulated complex spatiotemporal complicated potential and time-dependent -wave scattering length. These plots are generated with solution (31) and parameters , = −1, μ = 1, α = 0.2, υ = 0.5, ℓ(0) = 2, and two lens transformation parameters η() shown in (a). Plots (b) and (c) are, respectively, realized with γ() = 0.1 + cos (1.1) (red curve in (a)) and γ() = −0.1 + cos (1.1) (blue curve in (a)).

Image of FIG. 2.
FIG. 2.

Effect of the functional phase-imprint parameter () (via the phase-imprint parameter α) on the dynamics of solitary waves in 1D BEC described by Eqs. (1) and (2) . We use solution (31) and the same parameters as in Fig. 1 to realize plots (a) and (b). Here, we use (a) γ() = 0.1 + cos (1.1) and (b) γ() = −0.1 + cos (1.1).

Image of FIG. 3.
FIG. 3.

The dynamics of a solitary wave in a modulated complex spatiotemporal complicated potential and time-dependent -wave scattering length associated with Eq. (31) in the case of a time-independent strength of the magnetic trap with the same parameters as in Fig. 1 and = 0.005. (a) γ() = 0.1 + cos (1.1); (b) γ() = −0.1 + cos (1.1).

Image of FIG. 4.
FIG. 4.

The dynamics of a bright solitary wave in a spatiotemporal complex potential with a temporal periodic modulation of the strength of the magnetic trap () given by Eq. (18) with parameters = −0.02, = 0.1, = 0.98, . (a) γ() = 0.1 + 0.098 cos 1.1, (b) γ() = −0.1 + 0.098 cos 1.1, and (c) γ() = −0.31 + 0.098 cos 1.1. These plots are associated with the density |ψ(, )| obtained from solution (31) and with parameters = μ = 1, , ℓ(0) = 1, υ = 0.75, and α = 0.495.

Image of FIG. 5.
FIG. 5.

Effect of the functional phase-imprint parameter () on the dynamics of solitary waves in the case of a temporal periodic modulation of the strength of the magnetic trap () given by Eq. (18) with the same parameters values as in Fig. 4 . (a) γ() = 0.1 + 0.098 cos 1.1, (b) γ() = −0.31 + 0.098cos 1.1. The two plots are realized with density |ψ(, )| obtained from solution (31) at time = 5 and with parameters = μ = 1, , ℓ(0) = 1, υ = 0.75.

Image of FIG. 6.
FIG. 6.

The density of bright solitary waves given by Eq. (39) for |ψ(, )| with the temporal periodic modulation of the strength of the magnetic trap () given by Eq. (18) with the parameters = 0.1, = 0.2, = 0.98, and . The parameters chosen to generate these plots are ℓ(0) = 1, γ(0) = 0, = 1, ρ = 1.1, = 0.1, ω = −4, υ = 0.75, μ = 1, = 1, γ() = γ + 0.098 cos (1.1): (a) γ = 0.1, α = 0.1, ; (b) γ = 0.1, α = 0.1, ; (c) γ = −0.1, α = 0.1, ; (d) γ = −0.1, α = 0.1, .

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/content/aip/journal/jmp/54/5/10.1063/1.4803458
2013-05-07
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Exact wave solutions for Bose–Einstein condensates with time-dependent scattering length and spatiotemporal complicated potential
http://aip.metastore.ingenta.com/content/aip/journal/jmp/54/5/10.1063/1.4803458
10.1063/1.4803458
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