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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.
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关键词:
- 非线性Schrdinger方程 /
- 动力学性质 /
- 孤子 /
- 辛算法
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.-
Keywords:
- nonlinear Schrdinger equation /
- dynamical property /
- soliton /
- symplectic method
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[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
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[40] Khler T 2002 Phys. Rev. Lett. 89 210404
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