Figure 1

Motion of the center of a dark soliton in the presence of the magnetic trap with $\Omega =0.025$ and the optical lattice with $V_0=0.2$ and $k=1$. The three soliton trajectories correspond to different initial positions and optical lattice phases: $x_0\left(0\right)=0.1$ and $\theta =\pi ∕2$ (solid line), $x_0\left(0\right)=0$ and $\theta =0$ (dashed line), and $x_0\left(0\right)=0.01$ and $\theta =\pi ∕2$ (thin solid line).Reuse & Permissions

Figure 2

Entrapment of the moving dark soliton by a potential well belonging to the time-modulated optical lattice. The soliton is initially located at $x_0\left(0\right)=-3\pi ∕2$. The parameters are $\Omega =0.025,V_0=0.07,k=1,t_0=177$, and $T=5$. The dotted/solid line corresponds to the DS trajectory in the absence/presence of the time-modulated optical lattice. After getting trapped in the potential, the dark soliton stays there, performing small oscillations, during the time interval $177<t<650$; later, it escapes due to radiation loss.Reuse & Permissions

Figure 3

The targeted transfer of a dark soliton from its initial position, ${\eta }_i=-3\pi ∕2$, to the final one, ${\eta }_f=\pi ∕2$. The continuous and dashed curves show, respectively, the actual motion law of the trapped dark soliton, and that of the optical lattice drive. The strength of the parabolic trap is $\Omega =0.025$, the optical lattice parameters are $V_0=0.07$ and $k=1$, and the drive is taken in the form of Eqs. (7, 8) with $t_0=100$ and $T=60$. The dark soliton delivered by the moving optical lattice to the required destination stays there, performing small oscillations, during the time interval $200<t<400$; later, it escapes due to radiation loss.Reuse & Permissions