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Sinh-Gordon方程的同伦近似解

叶望川 李彪 王佳

引用本文:
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Sinh-Gordon方程的同伦近似解

叶望川, 李彪, 王佳

Approximate solution to Sinh-Gordon equation via the homotopy analysis method

Ye Wang-Chuan, Li Biao, Wang Jia
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  • 本文利用同伦分析方法得到了Sinh-Gordon方程的近似解.在所得到的解中包含一个辅助参数,可以有效地控制级数解的收敛范围和收敛速度.
    In this paper, approximate solution of the Sinh-Gordon equation is obtained via the homotopy analysis method. The obtained solution contains an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions.
    • 基金项目: 浙江自然科学基金(批准号:Y6090592),国家自然科学基金(批准号:10735030),宁波自然科学基金(批准号:2009B21003)和宁波大学王宽诚基金资助的课题.
    [1]

    Ablowitz M J, Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (New York: Cambridge Univ. Press)

    [2]

    Li Y S 1999 Soliton and integrable system (Shanghai: Shanghai Sci. Edu. Press) (in Chinese)

    [3]

    Weiss J, Tabor M, Carnevale G 1983 J. Math. Phys. 24 522

    [4]

    Malfliet W 1992 Am. J. Phys. 60 650

    [5]

    Parkes E J, Duffy B R 1996 Comput. Phys. Commun. 98 288

    [6]

    Lai S Y, Guo Y X, Qing Y, Wu Y H 2009 Chin. Phys. B 18 405

    [7]

    Fan E G 2002 Phys. Lett. A 294 26

    [8]

    Yan Z Y 2001 Phys. Lett. A 292 100

    [9]

    Li B 2007 Int. J. Mod. Phys. C 18 1187

    [10]

    Zhang S Q 2008 Acta Phys. Sin. 57 1335 (in Chinese) [张善卿 2008 物理学报 57 1335]

    [11]

    Li W, Liu S B, Yang W 2010 Chin. Phys. B 19 030307

    [12]

    Gu Y Q 2010 Chin. Phys. B 19 030402

    [13]

    Yao R X, Jiao X Y, Lou S Y 2009 Chin. Phys. B 18 1821

    [14]

    Jiao X Y, Lou S Y 2009 Chin. Phys. B 18 3611

    [15]

    Li J H, Lou S Y 2008 Chin. Phys. B 17 747

    [16]

    Wang J, Li B 2009 Chin. Phys. B 18 2109

    [17]

    Zhang H P, Chen Y, Li B 2009 Acta Phys. Sin. 58 7393 (in Chinese) [张焕萍、陈 勇、李 彪 2009 物理学报 58 7393]

    [18]

    Wang Y F, Lou S Y 2010 Chin. Phys. B 19 091128

    [19]

    Hu X R, Chen Y 2010 Chin. Phys. B 19 091982

    [20]

    Dong Z Z, Lang Y H, Chen Y 2010 Chin. Phys. B 19 091846

    [21]

    Tang X Y, Lou S Y, Zhang Y 2002 Phys. Rev. E 66 046601 Tang X Y, Lou S Y 2003 Chin. Phys. Lett. 3 335

    [22]

    Zhang L, Zhang L F, Wu H Y, Li G 2010 Acta Phys. Sin. 59 44 (in Chinese) [张 亮、张立凤、吴海燕、李 刚 2010 物理学报 59 44]

    [23]

    Huang J J, Alatancang, Wang H 2009 Chin. Phys. B 18 3616 Hou G L, Alatancang 2008 Chin. Phys. B 17 2753

    [24]

    He G, Mei F X 2008 Acta Phys. Sin. 57 18 (in Chinese) [何 光、梅凤翔 2008 物理学报 57 18]

    [25]

    Liao S J 2003 Chapman and Hall/CRC Press, Boca Raton

    [26]

    Hayat T Khan M, Asghar S 2004 Acta. Mech. 168 213

    [27]

    Liao S J 2009 Commun. Nonlinear Sci. Numer. Simulat 14 983 Liao S J 2010 Commun. Nonlinear Sci. Numer. Simulat 15 2003

    [28]

    Niu Z, Wang C 2010 Commun. Nonlinear Sci. Numer. Simulat 15 2026

    [29]

    Wu W, Liao S J 2005 Chaos, Solitons & Fractals 26 177

    [30]

    Wu Y Y, Wang C, Liao S J 2005 Chaos, Solitons & Fractals 23 1733

    [31]

    Abbasbandy S, Magyari E, Shivanian E 2009 Commun. Nonlinear. Sci. Numer. Simulat 14 3530

    [32]

    Wang J, Li B, Ye WC 2010 Chin. Phys. B 19 030401

    [33]

    Liu X Z 2010 Chin. Phys. B 19 100019

    [34]

    Corrigan E E, Delius G W 1999 J. Phys. A: Math. Gen. 32 8601

    [35]

    Tang Y N, Xu W, Shen J W 2008 Commun. Nonlinear. Sci. Numer. Simulat 13 1048

    [36]

    Papa E, Tsvelik A M 1999 Phys. Rev. B 60 12752

    [37]

    Wazwaz A M 2005 Appl. Math. Comput. 167 1196

  • [1]

    Ablowitz M J, Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (New York: Cambridge Univ. Press)

    [2]

    Li Y S 1999 Soliton and integrable system (Shanghai: Shanghai Sci. Edu. Press) (in Chinese)

    [3]

    Weiss J, Tabor M, Carnevale G 1983 J. Math. Phys. 24 522

    [4]

    Malfliet W 1992 Am. J. Phys. 60 650

    [5]

    Parkes E J, Duffy B R 1996 Comput. Phys. Commun. 98 288

    [6]

    Lai S Y, Guo Y X, Qing Y, Wu Y H 2009 Chin. Phys. B 18 405

    [7]

    Fan E G 2002 Phys. Lett. A 294 26

    [8]

    Yan Z Y 2001 Phys. Lett. A 292 100

    [9]

    Li B 2007 Int. J. Mod. Phys. C 18 1187

    [10]

    Zhang S Q 2008 Acta Phys. Sin. 57 1335 (in Chinese) [张善卿 2008 物理学报 57 1335]

    [11]

    Li W, Liu S B, Yang W 2010 Chin. Phys. B 19 030307

    [12]

    Gu Y Q 2010 Chin. Phys. B 19 030402

    [13]

    Yao R X, Jiao X Y, Lou S Y 2009 Chin. Phys. B 18 1821

    [14]

    Jiao X Y, Lou S Y 2009 Chin. Phys. B 18 3611

    [15]

    Li J H, Lou S Y 2008 Chin. Phys. B 17 747

    [16]

    Wang J, Li B 2009 Chin. Phys. B 18 2109

    [17]

    Zhang H P, Chen Y, Li B 2009 Acta Phys. Sin. 58 7393 (in Chinese) [张焕萍、陈 勇、李 彪 2009 物理学报 58 7393]

    [18]

    Wang Y F, Lou S Y 2010 Chin. Phys. B 19 091128

    [19]

    Hu X R, Chen Y 2010 Chin. Phys. B 19 091982

    [20]

    Dong Z Z, Lang Y H, Chen Y 2010 Chin. Phys. B 19 091846

    [21]

    Tang X Y, Lou S Y, Zhang Y 2002 Phys. Rev. E 66 046601 Tang X Y, Lou S Y 2003 Chin. Phys. Lett. 3 335

    [22]

    Zhang L, Zhang L F, Wu H Y, Li G 2010 Acta Phys. Sin. 59 44 (in Chinese) [张 亮、张立凤、吴海燕、李 刚 2010 物理学报 59 44]

    [23]

    Huang J J, Alatancang, Wang H 2009 Chin. Phys. B 18 3616 Hou G L, Alatancang 2008 Chin. Phys. B 17 2753

    [24]

    He G, Mei F X 2008 Acta Phys. Sin. 57 18 (in Chinese) [何 光、梅凤翔 2008 物理学报 57 18]

    [25]

    Liao S J 2003 Chapman and Hall/CRC Press, Boca Raton

    [26]

    Hayat T Khan M, Asghar S 2004 Acta. Mech. 168 213

    [27]

    Liao S J 2009 Commun. Nonlinear Sci. Numer. Simulat 14 983 Liao S J 2010 Commun. Nonlinear Sci. Numer. Simulat 15 2003

    [28]

    Niu Z, Wang C 2010 Commun. Nonlinear Sci. Numer. Simulat 15 2026

    [29]

    Wu W, Liao S J 2005 Chaos, Solitons & Fractals 26 177

    [30]

    Wu Y Y, Wang C, Liao S J 2005 Chaos, Solitons & Fractals 23 1733

    [31]

    Abbasbandy S, Magyari E, Shivanian E 2009 Commun. Nonlinear. Sci. Numer. Simulat 14 3530

    [32]

    Wang J, Li B, Ye WC 2010 Chin. Phys. B 19 030401

    [33]

    Liu X Z 2010 Chin. Phys. B 19 100019

    [34]

    Corrigan E E, Delius G W 1999 J. Phys. A: Math. Gen. 32 8601

    [35]

    Tang Y N, Xu W, Shen J W 2008 Commun. Nonlinear. Sci. Numer. Simulat 13 1048

    [36]

    Papa E, Tsvelik A M 1999 Phys. Rev. B 60 12752

    [37]

    Wazwaz A M 2005 Appl. Math. Comput. 167 1196

计量
  • 文章访问数:  7803
  • PDF下载量:  699
  • 被引次数: 0
出版历程
  • 收稿日期:  2010-04-28
  • 修回日期:  2010-05-06
  • 刊出日期:  2011-03-15

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