Abstract The ring dark solitons and their head-on collisions in a Bose--Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincaré--Lighthill--Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate $r$ according to the $r^{-1/3}$ law and depend on the initial soliton amplitude and radius.
Received: 31 October 2005
Revised: 09 March 2006
Accepted manuscript online:
PACS:
03.75.Lm
(Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)
Fund: Project supported by the National
Natural Science Foundation of China (Grant Nos 10347006 and 10475066),
and by the Natural\linebreak
\makebox[1.6mm]{}Science Foundation of Gansu province (Grant No
3ZS051-A25-013).
Cite this article:
Xue Ju-Kui (薛具奎), Peng Ping (彭娉) Head-on collision of ring dark solitons in Bose--Einstein condensates 2006 Chinese Physics 15 1149
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