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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.
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Keywords:
- nonlinear Schrdinger equation /
- dynamical property /
- soliton /
- symplectic method
[1] 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] Liu H, Wei J Y, Lou S Y, He X T 2008 Acta Phys. Sin. 57 1343 (in Chinese)
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[1] 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] Liu H, Wei J Y, Lou S Y, He X T 2008 Acta Phys. Sin. 57 1343 (in Chinese)
[44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85]
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