| Exact analytical solutions of three-dimensional Gross-Pitaevskii equation with time-space modulation |
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| 引用本文： | 胡晓,李彪. Exact analytical solutions of three-dimensional Gross-Pitaevskii equation with time-space modulation[J]. 中国物理 B, 2011, 20(5): 50315-050315 |
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| 作者姓名： | 胡晓 李彪 |
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| 作者单位： | Nonlinear Science Center and Department of Mathematics,Ningbo University |
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| 基金项目： | Project supported by Zhejiang Provincial Natural Science Foundations of China (Grant No. Y6090592), National Natural Science Foundation of China (Grant Nos. 11041003 and 10735030), Ningbo Natural Science Foundation (Grant Nos. 2010A610095, 2010A610103, an |
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| 摘 要： | By the generalized sub-equation expansion method and symbolic computation,this paper investigates the(3 + 1)dimensional Gross-Pitaevskii equation with time-and space-dependent potential,time-dependent nonlinearity,and gain or loss.As a result,rich exact analytical solutions are obtained,which include bright and dark solitons,Jacobi elliptic function solutions and Weierstrass elliptic function solutions.With computer simulation,the main evolution features of some of these solutions are shown by some figures.Nonlinear dynamics of a soliton pulse is also investigated under the different regimes of soliton management.
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| 关 键 词： | Gross-Pitaevskii equation soliton solutions Bose-Einstein condensate symbolic computation |
| 收稿时间： | 2010-11-23 |
Exact analytical solutions of three-dimensional Gross–Pitaevskii equation with time–space modulation |
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| Hu Xiao and Li Biao. Exact analytical solutions of three-dimensional Gross–Pitaevskii equation with time–space modulation[J]. Chinese Physics B, 2011, 20(5): 50315-050315 |
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| Authors: | Hu Xiao and Li Biao |
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| Affiliation: | Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China;Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China |
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| Abstract: | By the generalized sub-equation expansion method and symbolic computation, this paper investigates the (3+1)-dimensional Gross–Pitaevskii equation with time- and space-dependent potential, time-dependent nonlinearity, and gain or loss. As a result, rich exact analytical solutions are obtained, which include bright and dark solitons, Jacobi elliptic function solutions and Weierstrass elliptic function solutions. With computer simulation, the main evolution features of some of these solutions are shown by some figures. Nonlinear dynamics of a soliton pulse is also investigated under the different regimes of soliton management. |
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| Keywords: | Gross–Pitaevskii equation soliton solutions Bose–Einstein condensate symbolic computation |
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