Chin. Phys. Lett.  2017, Vol. 34 Issue (6): 060202    DOI: 10.1088/0256-307X/34/6/060202
GENERAL |
A High-Order Conservative Numerical Method for Gross–Pitaevskii Equation with Time-Varying Coefficients in Modeling BEC
Xiang Li1, Xu Qian1,2**, Ling-Yan Tang1, Song-He Song1
1College of Science and State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073
2Academy of Ocean Science and Engineering, National University of Defense Technology, Changsha 410073
Cite this article:   
Xiang Li, Xu Qian, Ling-Yan Tang et al  2017 Chin. Phys. Lett. 34 060202
Download: PDF(1906KB)   PDF(mobile)(1904KB)   HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract We propose a high-order conservative method for the nonlinear Schrödinger/Gross–Pitaevskii equation with time-varying coefficients in modeling Bose–Einstein condensation (BEC). This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.
Received: 05 January 2017      Published: 23 May 2017
PACS:  02.60.Lj (Ordinary and partial differential equations; boundary value problems)  
  02.70.Bf (Finite-difference methods)  
  02.60.Cb (Numerical simulation; solution of equations)  
  02.60.Jh (Numerical differentiation and integration)  
Fund: Supported by the National Natural Science Foundation of China under Grant Nos 11571366 and 11501570, the Open Foundation of State Key Laboratory of High Performance Computing of China, the Research Fund of National University of Defense Technology under Grant No JC15-02-02, and the Fund from HPCL.
TRENDMD:   
URL:  
https://cpl.iphy.ac.cn/10.1088/0256-307X/34/6/060202       OR      https://cpl.iphy.ac.cn/Y2017/V34/I6/060202
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
Xiang Li
Xu Qian
Ling-Yan Tang
Song-He Song
[1]Kunze M 1999 Physica D 128 273
[2]Kivshar Y S, Alexander T J and Turitsyn S K 2001 Phys. Lett. A 278 225
[3]Mallory K and Van Gorder R A 2014 Phys. Rev. E 89 013204
[4]Hong J L and Kong L H 2010 Commun. Comput. Phys. 7 613
[5]Bao W Z and Shen J 2005 SIAM J. Sci. Comput. 26 2010
[6]Dehghan M and Taleei A 2010 Comput. Phys. Commun. 181 43
[7]Zhou X F, Zhang S L, Zhou Z W, Malomed B A and Pu H 2012 Phys. Rev. A 85 023603
[8]Cartarius H and Wunner G 2012 Phys. Rev. A 86 013612
[9]D Agosta R and Presilla C 2002 Phys. Rev. A 65 043609
[10]Bronski J C, Carr L D, Deconinck B, Kutz J N and Promislow K 2001 Phys. Rev. E 63 036612
[11]Chen Y M, Song S H and Zhu H J 2012 Appl. Math. Comput. 218 5552
[12]Lv Z Q, Wang Y S and Song Y Z 2013 Chin. Phys. Lett. 30 030201
[13]Qian X, Fu H and Song S H 2016 Appl. Math. Comput. 307 1
[14]Hu W P, Deng Z and Yin T 2017 Commun. Nonlinear. Sci. 42 298
[15]Ma Y P, Kong L H and Hong J L 2011 Comput. Math. Appl. 61 319
[16]Qian X, Song S H, Gao E and Li W B 2012 Chin. Phys. B 21 070206
[17]Cai J X and Wang Y S 2013 Chin. Phys. B 22 060207
[18]Quispel G R W and McLaren D I 2008 J. Phys. A 41 045206
[19]Celledoni E, Grimm V, McLachlan R I, McLaren D, O Neale D, Owren B and Quispel G 2012 J. Comput. Phys. 231 6770
[20]Zhang H, Song S H, Chen X D and Zhou W E 2014 Chin. Phys. B 23 070208
[21]Jiang C L and Sun J Q 2014 Chin. Phys. B 23 050202
[22]Cai J X, Wang Y and Gong Y 2015 J. Sci. Comput. 1 36
Related articles from Frontiers Journals
[1] Long Xiong, Wei-Feng Zhuang, and Ming Gong. Dynamics of Quantum State and Effective Hamiltonian with Vector Differential Form of Motion Method[J]. Chin. Phys. Lett., 2022, 39(7): 060202
[2] Xiang Li, Xu Qian, Bo-Ya Zhang, Song-He Song. A Multi-Symplectic Compact Method for the Two-Component Camassa–Holm Equation with Singular Solutions[J]. Chin. Phys. Lett., 2017, 34(9): 060202
[3] CAI Wen-Jun, WANG Yu-Shun, SONG Yong-Zhong. Numerical Simulation of Rogue Waves by the Local Discontinuous Galerkin Method[J]. Chin. Phys. Lett., 2014, 31(04): 060202
[4] WANG Xing, MA Tian-Bao, NING Jian-Guo. A Pseudo Arc-Length Method for Numerical Simulation of Shock Waves[J]. Chin. Phys. Lett., 2014, 31(03): 060202
[5] HOU Shen-Yong, YU Sheng, LI Hong-Fu. Ohmic Losses in Coaxial Cavity Gyrotron with Outer Corrugation [J]. Chin. Phys. Lett., 2013, 30(12): 060202
[6] F. Khaksar Haghani, S. Karimi Vanani, J. Sedighi Hafshejani. Numerical Computation of the Tau Approximation for the Delayed Burgers Equation[J]. Chin. Phys. Lett., 2013, 30(2): 060202
[7] ZOU Li, ZOU Dong-Yang, WANG Zhen, ZONG Zhi. Finding Discontinuous Solutions to the Differential-Difference Equations by the Homotopy Analysis Method[J]. Chin. Phys. Lett., 2013, 30(2): 060202
[8] A. Yildirim, A. Gökdoğan, M. Merdan, V. Lakshminarayanan. Numerical Approximations to the Solution of Ray Tracing through the Crystalline Lens[J]. Chin. Phys. Lett., 2012, 29(7): 060202
[9] PAN Feng, XIE Ming-Xia, SHI Chang-Liang, J. P. DRAAYER. Quasi-exactly Solvable Cases of the N-Dimensional Symmetric Quartic Anharmonic Oscillator[J]. Chin. Phys. Lett., 2012, 29(7): 060202
[10] S. S. Dehcheshmeh*,S. Karimi Vanani,J. S. Hafshejani. Operational Tau Approximation for the Fokker–Planck Equation[J]. Chin. Phys. Lett., 2012, 29(4): 060202
[11] Junaid Ali Khan**, Muhammad Asif Zahoor Raja**, Ijaz Mansoor Qureshi . Novel Approach for a van der Pol Oscillator in the Continuous Time Domain[J]. Chin. Phys. Lett., 2011, 28(11): 060202
[12] SI Xin-Hui**, ZHENG Lian-Cun, ZHANG Xin-Xin, SI Xin-Yi, YANG Jian-Hong . Flow of a Viscoelastic Fluid through a Porous Channel with Expanding or Contracting Walls[J]. Chin. Phys. Lett., 2011, 28(4): 060202
[13] Junaid Ali Khan*, Muhammad Asif Zahoor Raja**, Ijaz Mansoor Qureshi . Stochastic Computational Approach for Complex Nonlinear Ordinary Differential Equations[J]. Chin. Phys. Lett., 2011, 28(2): 060202
[14] FENG Jun-Sheng**, LIU Zheng, GUO Jian-You . Bound and Resonant States of the Hulthén Potential Investigated by Using the Complex Scaling Method with the Oscillator Basis[J]. Chin. Phys. Lett., 2010, 27(11): 060202
[15] ZHANG Zhan-Long, DENG Jun, XIAO Dong-Ping, HE Wei, TANG Ju. An Adaptive Fast Multipole Higher Order Boundary Element Method for Power Frequency Electric Field of Substation[J]. Chin. Phys. Lett., 2010, 27(3): 060202
Viewed
Full text


Abstract