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Chin. Phys. B, 2011, Vol. 20(11): 114219    DOI: 10.1088/1674-1056/20/11/114219
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Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients

Liu Xiao-Bei(刘晓蓓) and Li Biao(李彪)
Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China
Abstract  We present three families of soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters. Different shapes of bright solitons, a train of bright solitons and dark solitons are observed. The obtained results may raise the possibilities of relevant experiments and potential applications.
Keywords:  (3+1)-dimensional nonlinear Sch?dinger Equation      optical soliton      soliton propagation  
Received:  11 April 2011      Revised:  26 May 2011      Accepted manuscript online: 
PACS:  42.81.Dp (Propagation, scattering, and losses; solitons)  
  02.30.Jr (Partial differential equations)  
  05.45.Yv (Solitons)  
Fund: Project supported by the Zhejiang Provincial Natural Science Foundations, China (Grant No. Y6090592), the National Natural Science Foundation of China (Grant Nos. 11041003 and 10735030), the Ningbo Natural Science Foundation, China (Grant Nos. 2010A610095, 2010A610103, and 2009B21003), and K.C. Wong Magna Fund in Ningbo University, China.

Cite this article: 

Liu Xiao-Bei(刘晓蓓) and Li Biao(李彪) Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients 2011 Chin. Phys. B 20 114219

[1] Zabusky N J and Kruskal M D 1965 Phys. Rev. Lett. 15 240
[2] Drazin P G and Johnson R S 1996 Solitons: an Introduction (Cambridge: Cambridge University Press)
[3] Ablowitz M J and Clarkson P A 1991 Soliton, Nonlinear Evolution Equations and Inverse Scattering (New York: Cambridge University Press)
[4] Gu C H, Hu H S and Zhou Z X 1999 Darboux Transformation in Soliton Theory and Its Geometric Applications (Shanghai: Shanghai Scientific and Technical Press) (in Chinese)
[5] Hirota R 2004 The Direct Method in Soliton Theory (Cambridge: Cambridge University Press)
[6] Wazwaz A M 2009 Partial Differential Equations and Solitary Waves Theory (Springer: High Education Press)
[7] Adomian G 1994 Solving Frontier Problems of Physics: The Decomposition Method (Boston: Kluwer Academic Publishers)
[8] Li Z B and Liu Y P 2002 Comput. Phys. Commun. 148 256
[9] Fan E 2000 Phys. Lett. A 277 212
[10] Li B, Chen Y and Zhang H Q 2002 J. Phys. A 35 8253
[11] Gao Y T and Tian B 2001 Comput. Phys. Commun. 133 158
[12] Fan E G 2003 J. Phys. A 36 7009
[13] Li B, Chen Y and Li Y Q 2008 Z. Naturforsch. 63a 763
[14] Serkin V and Hasegawa A 2000 Phys. Rev. Lett. 85 4502
[15] Ponomarenko S A and Agrawal G P 2006 Phys. Rev. Lett. 97 013901
[16] Serkin V N, Hasegawa A and Belyaeva T L 2007 Phys. Rev. Lett. 98 074102
[17] Wang J, Li B and Ye W C 2010 Commun. Theor. Phys. 53 698
[18] Hasegawa A and Kodama Y 1995 Solitons in Optical Communications (Oxford: Oxford University Press)
[19] Li L, Li Z H, Li S Q and Zhou G S 2004 Opt. Commun. 234 169
[20] Li Z D, Li Q Y, He P B, Bai Z G and Sun Y B 2007 Ann. Phys. 322 2945
[21] Zhang H P, Li B and Chen Y 2010 Chin. Phys. B 19 060302
[22] Li B 2007 Int. J. Mod. Phys. C 18 1187
[23] Li H M, Li Y S and Lin J 2009 Chin. Phys. B 18 3657
[24] Wang H and Li B 2011 Chin. Phys. B 20 040203
[25] Zhang H P, Li B, Chen Y and Huang F 2010 Chin. Phys. B 19 020201
[26] Anderson M H, Ensher J R, Matthews M R, Wieman C E and Cornell E A 1995 Science 269 198
[27] Bradley C C, Sackett C A, Tollett J J and Hulet R G 1995 Phys. Rev. Lett. 75 1687
[28] Davis K B, Mewes M O, Andrews M R, van Druten N J, Durfee D S, Kurn D M and Ketterle W 1995 Phys. Rev. Lett. 75 3969
[29] Dalfovo F, Giorgini F, Pitaevskii L P and Stringari S 1999 Rev. Mod. Phys. 71 463
[30] Lü B B, Hao X and Tian Q 2011 Chin. Phys. B 20 020308
[31] Wang Z X, Ni Z G, Cong F Z, Liu X S and Chen L 2010 Chin. Phys. B 19 113205
[32] Wang B, Tan L, Lü C H and Tan W T 2010 Chin. Phys. B 19 117402
[33] Li B, Zhang X F, Li Y Q, Chen Y and Liu W M 2008 Phys. Rev. A 78 023608
[34] Qi R, Yu X L, Li Z B and Liu W M 2009 Phys. Rev. Lett. 102 185301
[34] Hu X H, Zhang X F, Zhao D, Luo H G and Liu W M 2009 Phys. Rev. A 79 023619
[36] Wu L, Li L, Zhang J F, Mihalache D, Malomed B A and Liu W M 2010 Phys. Rev. A 81 061805(R)
[37] Hu X and Li B 2011 Chin. Phys. B 20 050315
[38] Yan Z Y and Konotop V V 2009 Phys. Rev. E 80 036607
[39] Yan Z Y and Hang C 2009 Phys. Rev. A 80 063626
[40] Gao Y and Lou S Y 2009 Commun. Thoer. Phys. 52 1031
[41] Zheng L and Tang Y 2010 Chin. Phys. B 19 044209
[42] Belic M, Nikola P, Zhong W P, Xie R H and Chen G 2008 Phys. Rev. Lett. 101 123904
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