Exact analytical solutions of three-dimensional Gross–Pitaevskii equation with time–space modulation

doi:10.1088/1674-1056/20/5/050315

中国物理B ›› 2011, Vol. 20 ›› Issue (5): 50315-050315.doi: 10.1088/1674-1056/20/5/050315

Exact analytical solutions of three-dimensional Gross–Pitaevskii equation with time–space modulation

胡晓, 李彪

Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China

收稿日期:2010-11-23 修回日期:2010-12-23 出版日期:2011-05-15 发布日期:2011-05-15
基金资助:
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

Exact analytical solutions of three-dimensional Gross–Pitaevskii equation with time–space modulation

Hu Xiao(胡晓) and Li Biao(李彪)

Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China

Received:2010-11-23 Revised:2010-12-23 Online:2011-05-15 Published:2011-05-15
Supported by:
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, and 2009B21003), and K.C. Wong Magna Fund in Ningbo University of China.

摘要/Abstract

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.

关键词: Gross–Pitaevskii equation, soliton solutions, Bose–Einstein condensate, symbolic computation

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.

Key words: Gross–Pitaevskii equation, soliton solutions, Bose–Einstein condensate, symbolic computation

中图分类号:

03.75.-b

05.45.Yv (Solitons) 31.15.-p (Calculations and mathematical techniques in atomic and molecular physics)

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.

Hu Xiao(胡晓) and Li Biao(李彪). Exact analytical solutions of three-dimensional Gross–Pitaevskii equation with time–space modulation[J]. Chin. Phys. B, 2011, 20(5): 50315-050315.

参考文献 33

[1]	Serkin V N and Hasegawa A 2000 Phys. Rev. Lett. 854502
[2]	Chen S and Yi L 2005 Phys. Rev. E 71 016606
[3]	Ponomarenko S A and Agrawal G P 2006 Phys. Rev. Lett.97 013901
[4]	Xie B H and Jing H 2002 Chin. Phys. 11 115
[5]	Huang G X 2004 Chin. Phys. 13 1866
[6]	Mu A X, Zhou X Y and Xue J K 2008 Chin. Phys. B 17764
[7]	Wang Z X, Ni Z G, Cong F Z, Liu X S and Chen L 2010Chin. Phys. B 19 113205
[8]	Wang B, Tan L, L?u C H and Tan W T 2010 Chin. Phys.B 19 117402
[9]	Li B, Zhang X F, Li Y Q, Chen Y and Liu W M 2008Phys. Rev. A 78 023608
[10]	Qi R, Yu X L, Li Z B and Liu W M 2009 Phys. Rev. Lett.102 185301
[11]	Hu X H, Zhang X F, Zhao D, Luo H G and Liu W M 2009Phys. Rev. A 79 023619
[12]	Yan Z Y, Chow K W and Malomed B A 2009 Chaos,Solitons and Fractals 42 3103
[13]	Yan Z Y and Konotop V V 2009 Phys. Rev. E 80 036607
[14]	Yan Z Y 2007 Phys. Lett. A 361 223
[15]	He Z M, Wang D L, Zhang W X, Wang F J and Ding JW 2008 Chin. Phys. B 17 3640
[16]	Xi Y D, Wang D L, He Z M and Ding J W 2009 Chin.Phys. B 18 939
[17]	Dalfovo F, Giorgini S, Pitaevskii L P and Stringari S 1999Rev. Mod. Phys. 71 463
[18]	Yan Z Y and Hang C 2009 Phys. Rev. A 80 063626
[19]	Muryshev A, Shlyapnikov G V, Ertmer W, Sengstock Kand Lewenstein M 2002 Phys. Rev. Lett. 89 110401
[20]	Lou S Y, Huang G X and Ruan H Y 1991 J. Phys. A 24L587
[21]	Fan E G 2000 Phys. Lett. A 277 212
[22]	Li H M 2005 Chin. Phys. 14 251
[23]	Chen Y, Li B and Zhang H Q 2004 Chin. Phys. 13 5
[24]	Zhu J M and Ma Z Y 2005 Chin. Phys. 14 17
[25]	Chen Y, Li B and Zhang H Q 2003 Chin. Phys. 12 940
[26]	Chen Y and Li B 2004 Chaos, Solitons and Fractals 19977
[27]	Li B, Chen Y, Xuan H N and Zhang H Q 2004 Appl. Math.Comput. 152 581
[28]	Chen Y, Yan Z Y, Li B and Zhang H Q 2003 Chin. Phys.12 1977
[29]	Zhi H Y, Zhao X Q and Zhang H Q 2005 Chin. Phys. 141296
[30]	Li B 2007 Int. J. Mod. Phys. C 18 1187
[31]	Zhang H P, Li B and Chen Y 2010 Chin. Phys. B 19060302
[32]	Zhang H P, Li B, Chen Y and Huang F 2010 Chin. Phys.B 19 020201
[33]	Tiesinga E, Williams C J, Julienne P S, Jones K M, LettP D and Phillips W D 1996 J. Res. Natl. Inst. Stand.Technol. 101 505

Exact analytical solutions of three-dimensional Gross–Pitaevskii equation with time–space modulation

Exact analytical solutions of three-dimensional Gross–Pitaevskii equation with time–space modulation

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 33

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Sha Li(李莎), Tiecheng Xia(夏铁成), and Hanyu Wei(魏含玉). Riemann--Hilbert approach of the complex Sharma—Tasso—Olver equation and its N-soliton solutions[J]. 中国物理B, 2023, 32(4): 40203-040203.
[2]	Xuefeng Zhang(张雪峰), Tao Xu(许韬), Min Li(李敏), and Yue Meng(孟悦). Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation[J]. 中国物理B, 2023, 32(1): 10505-010505.
[3]	Jun-Cai Pu(蒲俊才), Jun Li(李军), and Yong Chen(陈勇). Soliton, breather, and rogue wave solutions for solving the nonlinear Schrödinger equation using a deep learning method with physical constraints[J]. 中国物理B, 2021, 30(6): 60202-060202.
[4]	程雪苹, 马文秀, 杨云青. Lump-type solutions of a generalized Kadomtsev-Petviashvili equation in (3+1)-dimensions[J]. 中国物理B, 2019, 28(10): 100203-100203.
[5]	康周正, 夏铁成, 马茜. Multi-soliton solutions for the coupled modified nonlinear Schrödinger equations via Riemann-Hilbert approach[J]. 中国物理B, 2018, 27(7): 70201-070201.
[6]	徐思齐, 耿献国. N-soliton solutions for the nonlocal two-wave interaction system via the Riemann-Hilbert method[J]. 中国物理B, 2018, 27(12): 120202-120202.
[7]	李近元, 方念乔, 张吉, 薛玉龙, 王雪木, 袁晓博. (2+1)-dimensional dissipation nonlinear Schrödinger equation for envelope Rossby solitary waves and chirp effect[J]. 中国物理B, 2016, 25(4): 40202-040202.
[8]	贾仁需, 闫宏丽, 刘文军, 雷鸣. Periodic solitons in dispersion decreasingfibers with a cosine profile[J]. , 2014, 23(10): 100502-100502.
[9]	徐桂琼. Painlevé integrability of generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions[J]. 中国物理B, 2013, 22(5): 50203-050203.
[10]	荆建春, 李彪. Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrödinger equation with variable coefficients[J]. Chin. Phys. B, 2013, 22(1): 10303-010303.
[11]	Etienne Wamba, Timoléon C. Kofané, Alidou Mohamadou . Matter-wave solutions of Bose–Einstein condensates with three-body interaction in linear magnetic and time-dependent laser fields[J]. 中国物理B, 2012, 21(7): 70504-070504.
[12]	张翼, 程智龙, 郝晓红. Riemann theta function periodic wave solutions for the variable-coefficient mKdV equation[J]. Chin. Phys. B, 2012, 21(12): 120203-120203.
[13]	张焕萍, 李彪, 陈勇. Some exact solutions to the inhomogeneous higher-order nonlinear Schr?dinger equation by a direct method[J]. 中国物理B, 2010, 19(6): 60302-060302.
[14]	陈春丽, 张近, 李翊神. Study on an extended Boussinesq equation[J]. 中国物理B, 2007, 16(8): 2167-2179.
[15]	刘官厅. The pth-order periodic solutions for a family of N-coupled nonlinear SchrOdingerequations[J]. 中国物理B, 2006, 15(11): 2500-2505.