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Chin. Phys. B, 2013, Vol. 22(10): 100507    DOI: 10.1088/1674-1056/22/10/100507
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Trial function method and exact solutions to the generalized nonlinear Schrödinger equation with time-dependent coefficient

Cao Rui (曹瑞)a b, Zhang Jian (张健)a
a College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China;
b Department of Mathematics, Heze University, Heze 274000, China
Abstract  In this paper, the trial function method is extended to study the generalized nonlinear Schrödinger equation with time-dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrödinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrödinger equation with time-dependent coefficients under constraint conditions.
Keywords:  generalized nonlinear Schrödinger equation      exact solution      trial function method  
Received:  24 December 2012      Revised:  18 April 2013      Accepted manuscript online: 
PACS:  05.45.Yv (Solitons)  
  02.30.Jr (Partial differential equations)  
  02.30.Hq (Ordinary differential equations)  
Fund: Project supported in part by the National Natural Science Foundation of China (Grant No. 11071177).
Corresponding Authors:  Cao Rui     E-mail:  ruicao999@126.com

Cite this article: 

Cao Rui (曹瑞), Zhang Jian (张健) Trial function method and exact solutions to the generalized nonlinear Schrödinger equation with time-dependent coefficient 2013 Chin. Phys. B 22 100507

[1] Newell A C 1985 Solitons in Mathematics and Physics (Philadelphia: SIAM)
[2] Ablowitz M J and Segur H 1981 Solitons and the Inverse Scattering Transformation (Philadelphia: SIAM)
[3] Hasegawa A and Kodama Y 1995 Solitons in Optical Communications (New York: Oxford University Press)
[4] Özis T and Yildirim A 2008 Chaos, Solitons and Fractals 38 209
[5] Zhang M, Ma Y L and Li B Q 2013 Chin. Phys. B 22 030511
[6] Miura M R 1978 Bäcklund Transformation (Berlin: Springer)
[7] Lin J 2002 Chin. Phys. Lett. 19 765
[8] Hirota R 1971 Phys. Rev. Lett. 27 1192
[9] Yao R X, Jiao X Y and Lou S Y 2009 Chin. Phys. B 18 1821
[10] Fan E G, Zhang H Q and Lin G 1998 Acta Phys. Sin. 47 1064 (in Chinese)
[11] Hu H C, Lou S Y and Liu Q P 2003 Chin. Phys. Lett. 20 1413
[12] Ying J P and Lou S Y 2003 Chin. Phys. Lett. 20 1448
[13] Li D S and Zhang H Q 2004 Acta Phys. Sin. 53 1639 (in Chinese)
[14] Wazwaz A M 2008 Chaos, Solitons and Fractals 37 1136
[15] Li D S and Zhang H Q 2004 Acta Phys. Sin. 53 1635 (in Chinese)
[16] Wazwaz A M 2005 Comput. Math. Appl. 50 1685
[17] Fan E G 2000 Phys. Lett. A 277 212
[18] Liu S K, Fu Z T, Liu S D and Zhao Q 2001 Phys. Lett. A 289 69
[19] Zhang L, Zhang L F and Li C Y 2008 Chin. Phys. B 17 403
[20] Fu Z T, Liu S K and Liu S D 2003 Acta Phys. Sin. 52 2949 (in Chinese)
[21] Shi L F, Chen C S and Zhou X C 2011 Chin. Phys. B 20 100507
[22] Liu C S 2005 Acta Phys. Sin 54 2505 (in Chinese)
[23] Liu C S 2006 Commun. Theor. Phys. 45 395
[24] Azzouzi F, Triki H, Mezghiche K and EI Akrmi A 2009 Chaos, Solitons and Fractals 39 1304
[25] Ma W X and Chen M 2009 Appl. Math. Comput. 215 2835
[26] Zhang L H and Si J G 2010 Commun. Nonlinear Sci. Numer. Simul. 15 2747
[27] Zhang H P, Li B and Chen Y 2010 Chin. Phys. B 19 060302
[28] Qi F H, Tian B, Lü X, Guo R and Xue Y S 2012 Commun. Nonlinear Sci. Numer. Simul. 17 2372
[29] Ebaid A and Khaled S M 2011 J. Comput. Appl. Math. 235 1984
[30] Zhang J L, Li B A and Wang M L 2009 Chaos, Solitons and Fractals 39 858
[31] Wang H and Li B 2011 Chin. Phys. B 20 040203
[32] Yan Z Y 2010 Phys. Lett. A 374 4838
[33] Zheng C L and Li Y 2012 Chin. Phys. B 21 070305
[34] Zhong W P, Belic M R and Huang T W 2013 Optik-International Journal for Light and Electron Optics 124 2397
[35] Taghizadeh N, Mirzazadeh M and Farahroot F 2011 Math. Anal. Appl. 374 549
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