Painlevé integrability of generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions

doi:10.1088/1674-1056/22/5/050203

Abstract By means of singularity structure analysis, the integrability of a generalized fifth-order KdV equation is investigated. It is proven that this equation passes the Painlevé test for integrability only for three distinct cases. Moreover, the multi-soliton solutions are presented for this equation under three sets of integrable conditions. Finally, by selecting appropriate parameters, we analyze the evolution of two solitons, which is especially interesting as it may describe the overtaking and the head-on collisions of solitary waves of different shapes and different types.

Keywords: generalized fifth-order KdV equation Painlevé integrability soliton solution symbolic computation

Received: 21 November 2012
Revised: 05 January 2013
Accepted manuscript online:

PACS:	02.30.Ik	(Integrable systems)
	05.45.Yv	(Solitons)
	02.30.Jr	(Partial differential equations)

Fund: Projects supported by the National Natural Science Foundation of China (Grant Nos. 11201290 and 71103118).

Corresponding Authors: Xu Gui-Qiong
E-mail: xugq@staff.shu.edu.cn

Cite this article:

Xu Gui-Qiong (徐桂琼) Painlevé integrability of generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions 2013 Chin. Phys. B 22 050203

[1]	Ablowitz M J and Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press)
[2]	Wadati M, Sanuki H and Konno K 1975 Prog. Theor. Phys. 53 419
[3]	Weiss J, Tabor M and Carnevale G 1983 J. Math. Phys. 24 522
[4]	Hirota R 1971 Phys. Rev. Lett. 27 1192
[5]	Zamir M 2000 The Physics of Pulsatile Flow (New York: Springer-Verlag)
[6]	Yan Z Y and Hang C 2009 Phys. Rev. A 80 063626
[7]	Yang Z, Ma S H and Fang J P 2011 Chin. Phys. B 20 040301
[8]	Yan Z Y and Jiang D M 2012 J. Math. Analy. Appl. 395 542
[9]	Dai H H and Huo Y 2002 Wave Motions. 35 55
[10]	Zhang Y, Li J B and Lv Y N 2008 Annals of Physics 323 3059
[11]	Zhang Y, Wei W W, Cheng T F and Song Y 2011 Chin. Phys. B 20 110204
[12]	Yang Y Q and Chen Y 2011 Chin. Phys. B 20 1674
[13]	Fan E G 2011 Phys. Lett. A 375 493
[14]	Serkin V N and Hasegawa A 2000 Phys. Rev. Lett. 85 4502
[15]	Xu G Q 2009 Comput. Phys. Commun. 180 1137
[16]	Zhang H P, Li B and Chen Y 2010 Chin. Phys. B 19 060302
[17]	Wang H and Li B 2011 Chin. Phys. B 20 040203
[18]	Zheng C L and Li Y 2012 Chin. Phys. B 21 070305
[19]	Zhao D, Zhang Y J, Lou W W and Luo H G 2011 J. Math. Phys. 52 043502
[20]	Yu X, Gao Y T, Sun Z Y and Liu Y 2010 Phys. Scr. 81 045402
[21]	Yu X, Gao Y T, Sun Z Y and Liu Y 2011 Commun. Theor. Phys. 55 629
[22]	Chen B and Xie Y C 2005 Chao. Soliton. Fract. 23 243
[23]	Zhang Y X, Zhang H Q, Li J, Xu T, Zhang C Y and Tian B 2008 Commun. Theor. Phys. 49 833
[24]	Wazwaz A M 2010 Phys. Scr. 82 035009
[25]	Hereman W, Göktas Ü, Colagrosso M D and Miller A 1998 Comput. Phys. Commun. 115 428
[26]	Lou S Y 1998 Phys. Rev. Lett. 80 5027
[27]	Sakovich S Yu and Tsuchida T 2000 J. Phys. A: Math. Gen. 33 7217
[28]	Baldwin D and Hereman W 2006 J. Nonlin. Math. Phys. 13 90
[29]	Lou S Y, Tong B, Hu H C and Tang X Y 2006 J. Phys. A: Math. Gen. 39 513
[30]	Xu G Q 2006 Phys. Rev. E 74 027602
[31]	Xu G Q 2008 Comput. Phys. Commun. 178 505
[32]	Ding C Y, Zhao D and Luo H G 2012 J. Phys. A: Math. Theor. 45 115203
[33]	Nakamura A 1979 J. Phys. Soc. Jpn. 47 1701
[34]	Hu X B and Clarkson P A 1995 J. Phys. A: Math. Gen. 28 5009
[35]	Gilson C R, Hu X B, Ma W X and Tam H W 2003 Phys. D 175 177
[36]	Zhang D J and Chen D Y 2004 J. Phys. A: Math. Gen. 37 851
[37]	Yao Y Q, Chen D Y and Zhang D J 2008 Phys. Lett. A 372 2017
[38]	Chen S T, Zhu X M, Li Q and Chen D Y 2011 Chin. Phys. Lett. 28 060202
[39]	Wu J P, Geng X G and Zhang X L 2009 Chin. Phys. Lett. 26 020202
[40]	Fan E G and Hon Y C 2008 Phys. Rev. E 78 036607
[41]	Fan E G and Chow K K 2011 J. Math. Phys. 52 023504
[42]	Xu G Q and Li Z B 2005 Appl. Math. Comput. 169 1364

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Painlevé integrability of generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions

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