Oblique Dark Solitons in Supersonic Flow of a Bose-Einstein Condensate

In the framework of the Gross-Pitaevskii mean field approach, it is shown that the supersonic flow of a Bose-Einstein condensate can support a new type of pattern—an oblique dark soliton. The corresponding exact solution of the Gross-Pitaevskii equation is obtained. It is demonstrated by numerical simulations that oblique solitons can be generated by an obstacle inserted into the flow.

Figure 1

Emergence of a pair of oblique dark solitons after “switching on” supersonic flow ($M=5$) past a disk-shaped impenetrable obstacle of radius $r=1$ located at $(x=0,y=0)$. The direction of the flow is from left to right. Density plots are shown for 3 times: $t=5$, $t=10$, and $t=20$. The dark structures correspond to oblique dark solitons, which, in turn, generate the vortex streets near the end points.

Figure 2

Cross sections of the density distributions for $x=20$ (dashed line), $x=60$ (solid line), and $y>0$ obtained from numerical solution of the GP equation (19). These are compared with soliton profiles (11) with slope $a=10$ shown as functions of $y$ at the same values of $x$ ($x=20$ corresponds to “crosses” and $x=60$ to “circles”).

Figure 3

Density plot at the moment $t=30$ for the supersonic flow ($M=5$) past a disk-shaped impenetrable obstacle with radius $r=5$ located at $(x=0,y=0)$.