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The modulational instability of the solition wave in two-dimensional Bose-Einstein condensates

Zhang Heng Duan Wen-Shan

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The modulational instability of the solition wave in two-dimensional Bose-Einstein condensates

Zhang Heng, Duan Wen-Shan
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  • The solition wave in Bose-Einstein condensate with disk-shaped trap is investigated in this paper. Beyond the mean field, a two-dimensional nonlinear Schrödinger equation is obtained. The modulational instability for this system is studied analytically, and the growth rate for it is given.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11275156).
    [1]

    Wen W, Shen S Q, Huang G X 2010 Phys. Rev. B 81 014528

    [2]

    Zang X F, Li J P, Tan L 2007 Acta Phys. Sin. 56 4348 (in Chinese) [臧小飞, 李菊萍, 谭磊2007 物理学报 56 4348]

    [3]

    Wang G F, Fu L B, Liu J 2006 Phys. Rev. A 73 13619

    [4]

    Li S C, Fu L B, Duan W S, Liu J 2008 Phys. Rev. A 78 063621

    [5]

    Wen W, Huang G X 2009 Phys. Rev. A 79 023605

    [6]

    Ma Y, Fu L B, Yang Z A, Liu J 2006 Acta Phys. Sin. 55 5623 (in Chinese) [马云, 傅立斌, 杨志安, 刘杰2006 物理学报 55 5623]

    [7]

    Madison K, Chevy F, Bretin V, Dalibard J 2000 Phys. Rev. Lett. 84 806

    [8]

    Svidzinsky A A, Fetter A L 2000 Phys. Rev. Lett. 84 5919

    [9]

    Jochin S, Bartenstein M, Altmeyer A, Hendl G, Hecker Denschlag J, Grimm R 2004 Phys. Rev. Lett. 91 240402

    [10]

    Wang G F, Fu L B, Liu J 2006 Phys. Rev. A 73 13619

    [11]

    Liu J, Wu B, Niu Q 2003 Phys. Rev. Lett. 90 170404

    [12]

    Wu Y, Yang X X 2003 Phys. Rev. A 68 013608

    [13]

    Hu B B, Huang G X, Ma Y L 2004 Phys. Rev. A 69 063608

    [14]

    Legget A J 2003 Rev. Mod. Phys. 75 1083

    [15]

    Trombettoni A, Smerzi A 2001 Phys. Rev. Lett. 86 2353

    [16]

    Gerton J M, Strekalov D, Prodan I, Hulet R G 2001 Nature 408 692

    [17]

    Men F D, Liu H, Fan Z L, Zhu H Y 2009 Chin. Phys. B 18 2649

    [18]

    Liu J, Fu L B, Ou B Y, Chen S G, Chin D, Wu B, Niu Q 2002 Phys. Rev. A 66 023404

    [19]

    Bradley C C, Sackett C A, Hulet R G 1997 Phys. Rev. Lett. 78 985

    [20]

    Huang G X 2001 Chin. Phys. Lett. 18 628

    [21]

    Yang X X, Shi Y R, Duan W S 2008 Commun. Theor. Phys. 49 119

    [22]

    Hang G X, Zhu S H 2002 Chin. Phys. Lett. 19 17

    [23]

    Duan W S, Chen J H, Yang H J, Shi Y R, Wang H Y 2006 Chin. Phys. Lett. 23 2000

    [24]

    Song S W, Wang D S, Wang H Q, Liu W M 2012 Phys. Rev. A 85 063617

    [25]

    Liang G Z, Han J N, Lin M M, Wei J N, Duan W S 2009 Phys. Plasmas 16 073705

    [26]

    Jiang X, Gao X Y, Li S C, Shi Y R, Duan W S 2009 Appl. Math. Comp. 214 60

    [27]

    Tian D X, He G J, Han J N, Duan W S 2009 Commun. Theor. Phys. 51 529

    [28]

    Li S C, Han J N, Duan W S 2009 Physica B 404 1235

    [29]

    Li S C, Duan W S 2008 Commun. Theor. Phys. 50 655

    [30]

    Li B, Zhang X F, Li Y Q, Chen Y, Liu W M 2008 Phys. Rev. A 78 023608

    [31]

    Hu X H, Zhang X F, Zhao D, Luo H G, Liu W M 2009 Phys. Rev. A 79 023619

    [32]

    Han J N, Du S L, Duan W S 2008 Phys. Plasmas 15 112104

    [33]

    Duan W S, Parkes J, Zhang L 2004 Phys. Plasmas 11 3762

    [34]

    Gammal A, Frederico T, Tomio L, Chomaz P 2000 Phys. Rev. A 61 051602

    [35]

    Kagan Y, Muryshev A E, Shlyapnikov G V 1998 Phys. Rev. Lett. 81 933

    [36]

    Dalfovo F, Giorgini S, Pitaevskii L, Stringari S 1999 Rev. Mod. Phys. 71 463

    [37]

    Duan W S, Parkes J, Lin M M 2005 Phys. Plasmas 12 022106

  • [1]

    Wen W, Shen S Q, Huang G X 2010 Phys. Rev. B 81 014528

    [2]

    Zang X F, Li J P, Tan L 2007 Acta Phys. Sin. 56 4348 (in Chinese) [臧小飞, 李菊萍, 谭磊2007 物理学报 56 4348]

    [3]

    Wang G F, Fu L B, Liu J 2006 Phys. Rev. A 73 13619

    [4]

    Li S C, Fu L B, Duan W S, Liu J 2008 Phys. Rev. A 78 063621

    [5]

    Wen W, Huang G X 2009 Phys. Rev. A 79 023605

    [6]

    Ma Y, Fu L B, Yang Z A, Liu J 2006 Acta Phys. Sin. 55 5623 (in Chinese) [马云, 傅立斌, 杨志安, 刘杰2006 物理学报 55 5623]

    [7]

    Madison K, Chevy F, Bretin V, Dalibard J 2000 Phys. Rev. Lett. 84 806

    [8]

    Svidzinsky A A, Fetter A L 2000 Phys. Rev. Lett. 84 5919

    [9]

    Jochin S, Bartenstein M, Altmeyer A, Hendl G, Hecker Denschlag J, Grimm R 2004 Phys. Rev. Lett. 91 240402

    [10]

    Wang G F, Fu L B, Liu J 2006 Phys. Rev. A 73 13619

    [11]

    Liu J, Wu B, Niu Q 2003 Phys. Rev. Lett. 90 170404

    [12]

    Wu Y, Yang X X 2003 Phys. Rev. A 68 013608

    [13]

    Hu B B, Huang G X, Ma Y L 2004 Phys. Rev. A 69 063608

    [14]

    Legget A J 2003 Rev. Mod. Phys. 75 1083

    [15]

    Trombettoni A, Smerzi A 2001 Phys. Rev. Lett. 86 2353

    [16]

    Gerton J M, Strekalov D, Prodan I, Hulet R G 2001 Nature 408 692

    [17]

    Men F D, Liu H, Fan Z L, Zhu H Y 2009 Chin. Phys. B 18 2649

    [18]

    Liu J, Fu L B, Ou B Y, Chen S G, Chin D, Wu B, Niu Q 2002 Phys. Rev. A 66 023404

    [19]

    Bradley C C, Sackett C A, Hulet R G 1997 Phys. Rev. Lett. 78 985

    [20]

    Huang G X 2001 Chin. Phys. Lett. 18 628

    [21]

    Yang X X, Shi Y R, Duan W S 2008 Commun. Theor. Phys. 49 119

    [22]

    Hang G X, Zhu S H 2002 Chin. Phys. Lett. 19 17

    [23]

    Duan W S, Chen J H, Yang H J, Shi Y R, Wang H Y 2006 Chin. Phys. Lett. 23 2000

    [24]

    Song S W, Wang D S, Wang H Q, Liu W M 2012 Phys. Rev. A 85 063617

    [25]

    Liang G Z, Han J N, Lin M M, Wei J N, Duan W S 2009 Phys. Plasmas 16 073705

    [26]

    Jiang X, Gao X Y, Li S C, Shi Y R, Duan W S 2009 Appl. Math. Comp. 214 60

    [27]

    Tian D X, He G J, Han J N, Duan W S 2009 Commun. Theor. Phys. 51 529

    [28]

    Li S C, Han J N, Duan W S 2009 Physica B 404 1235

    [29]

    Li S C, Duan W S 2008 Commun. Theor. Phys. 50 655

    [30]

    Li B, Zhang X F, Li Y Q, Chen Y, Liu W M 2008 Phys. Rev. A 78 023608

    [31]

    Hu X H, Zhang X F, Zhao D, Luo H G, Liu W M 2009 Phys. Rev. A 79 023619

    [32]

    Han J N, Du S L, Duan W S 2008 Phys. Plasmas 15 112104

    [33]

    Duan W S, Parkes J, Zhang L 2004 Phys. Plasmas 11 3762

    [34]

    Gammal A, Frederico T, Tomio L, Chomaz P 2000 Phys. Rev. A 61 051602

    [35]

    Kagan Y, Muryshev A E, Shlyapnikov G V 1998 Phys. Rev. Lett. 81 933

    [36]

    Dalfovo F, Giorgini S, Pitaevskii L, Stringari S 1999 Rev. Mod. Phys. 71 463

    [37]

    Duan W S, Parkes J, Lin M M 2005 Phys. Plasmas 12 022106

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  • Cited By: 0
Publishing process
  • Received Date:  27 August 2012
  • Accepted Date:  04 September 2012
  • Published Online:  05 February 2013

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