中国物理B ›› 2006, Vol. 15 ›› Issue (6): 1149-1153.doi: 10.1088/1009-1963/15/6/005

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Head-on collision of ring dark solitons in Bose--Einstein condensates

薛具奎, 彭娉   

  1. Physics and Electronics Engineering College,Northwest Normal University, Lanzhou 730070, China
  • 收稿日期:2005-10-31 修回日期:2006-03-09 出版日期:2006-06-20 发布日期:2006-06-20
  • 基金资助:
    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).

Head-on collision of ring dark solitons in Bose--Einstein condensates

Xue Ju-Kui (薛具奎), Peng Ping (彭娉)   

  1. Physics and Electronics Engineering College,Northwest Normal University, Lanzhou 730070, China
  • Received:2005-10-31 Revised:2006-03-09 Online:2006-06-20 Published:2006-06-20
  • Supported by:
    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).

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摘要： 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 Poincar\'e--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.

关键词: ring dark solitons, Bose-Einstein condensates, head-on collision

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.

Key words: ring dark solitons, Bose-Einstein condensates, head-on collision

中图分类号:  (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)

  • 03.75.Lm
02.30.Em (Potential theory) 02.30.Jr (Partial differential equations) 05.30.Jp (Boson systems)