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立方五次方非线性Schrodinger方程的动力学性质研究

花巍 刘学深

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立方五次方非线性Schrodinger方程的动力学性质研究

花巍, 刘学深

Dynamics of cubic and quintic nonlinear Schrdinger equations

Hua Wei, Liu Xue-Shen
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  • 采用辛算法数值求解了一维立方五次方非线性Schrdinger方程,研究了不同非线性参数下非线性Schrdinger方程的动力学性质.数值结果表明,随着立方非线性参数的增加,系统经历了拟周期状态、混沌状态和周期状态,且在五次方项的调制下,呼吸子解可以退化为单孤子解.
    We solve one-dimensional(1D) cubic and quintic nonlinear Schrdinger equations by the symplectic method. The dynamical property of the nonlinear Schrdinger equation is studied with using diffenent nonlinear coefficients. The results show that the system presents quasiperiodic solution, chaotic solution, and periodic solution with the cubic nonlinear coefficient increasing, and the breather solution reduced into a fundamental soliton solution under the modulation of the quintic nonlinear coefficient.
    • 基金项目: 国家自然科学基金(批准号:10974068,11174108)资助的课题.
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    Kim J I, Park H K, Moon H T 1997 Phys. Rev. E 55 3948

    [2]

    Tajiri M, Watanabe Y 1998 Phys. Rev. E 57 3510

    [3]
    [4]
    [5]

    Muslu G M, Erbay H A 2005 Math. Comput. Simulat. 67 581

    [6]
    [7]

    Dehghan M, Taleei A 2010 Comput. Phys. Commun. 181 43

    [8]
    [9]

    Cai D, Bishop A R, Grnbech J, Malomed B A 1994 Phys. Rev. E 49 R1000

    [10]
    [11]

    Zong F D, Yang Y, Zhang J F 2009 Acta Phys. Sin. 58 3670 (in Chinese)

    [12]
    [13]

    Zheng X P, Lin J, Han P 2010 Acta Phys. Sin. 59 6752 (in Chinese)

    [14]
    [15]

    Liu H, He X T, Lou S Y 2002 Chin. Phys. Lett. 19 87

    [16]
    [17]

    Sun J Q, Gu X Y, Ma Z Q 2004 Chin. J. Comput. Phys. 21 321(in Chinese)

    [18]
    [19]

    Qiao B, Zhou C T, He X T, Lai C H 2008 Commun. Comput. Phys. 4 1129

    [20]
    [21]

    Liu X S, Ding P Z 2004 J. Phys. A 37 1589

    [22]

    Luo X Y, Liu X S, Ding P Z 2007 Acta Phys. Sin. 56 604 (in Chinese)

    [23]
    [24]
    [25]

    Liu X S, Qi Y Y, Ding P Z 2004 Chin. Phys. Lett. 21 2081

    [26]

    Luo X Y, Liu X S, Ding P Z 2007 J. At. Mol. Phys. 24 418(in Chinese)

    [27]
    [28]
    [29]

    Chang Q S, Jia E, Sun W 1999 J. Comput. Phys. 148 397

    [30]

    Muruganandam P, Adhikari S K 2009 Comput. Phys. Commun. 180 1888

    [31]
    [32]
    [33]

    Feng K 1986 J. Comput. Math. 4 279

    [34]

    Tang Y F, Vzquez L, Zhang F, Prez-Garca V M 1996 Comput. Math. Applic. 32 73

    [35]
    [36]

    Sun J Q, Ma Z Q, Hua W, Qin M Z 2006 Appl. Math. Comput. 177 446

    [37]
    [38]
    [39]

    Liu X S, Qi Y Y, He J F, Ding P Z 2007 Commun. Comput. Phys. 2 1

    [40]

    Khler T 2002 Phys. Rev. Lett. 89 210404

    [41]
    [42]
    [43]

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计量
  • 文章访问数:  6591
  • PDF下载量:  781
  • 被引次数: 0
出版历程
  • 收稿日期:  2010-12-31
  • 修回日期:  2011-02-18
  • 刊出日期:  2011-11-15

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