Integrability of extended (2+1)-dimensional shallow water wave equation with Bell polynomials

doi:10.1088/1674-1056/22/5/050509

Abstract We investigate the extended (2+1)-dimensional shallow water wave equation. The binary Bell polynomials are used to construct bilinear equation, bilinear Bäcklund transformation, Lax pair, and Darboux covariant Lax pair for this equation. Moreover, the infinite conservation laws of this equation are found by using its Lax pair. All conserved densities and fluxes are given with explicit recursion formulas. The N-soliton solutions are also presented by means of the Hirota bilinear method.

Keywords: binary Bell polynomials, Darboux covariant Lax pair, bilinear Bäcklund transformation infinite conservation laws

Received: 28 September 2012
Revised: 13 November 2012
Accepted manuscript online:

PACS:	05.45.Yv	(Solitons)
	02.30.Ik	(Integrable systems)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11075055 and 11275072), the Innovative Research Team Program of the National Natural Science Foundation of China (Grant No. 61021004), the Shanghai Knowledge Service Platform for Trustworthy Internet of Things, China (Grant No. ZF1213), and the National High Technology Research and Development Program of China (Grant No. 2011AA010101).

Corresponding Authors: Chen Yong
E-mail: ychen@sei.ecnu.edu.cn

Cite this article:

Wang Yun-Hu (王云虎), Chen Yong (陈勇) Integrability of extended (2+1)-dimensional shallow water wave equation with Bell polynomials 2013 Chin. Phys. B 22 050509

[1]	Hirota R 2004 Direct Methods in Soliton Theory (Berlin: Springer-Verlag)
[2]	Hu X B 1993 J. Phys. A: Math. Gen. 26 L465
[3]	Zuo J M and Zuo Y M 2011 Chin. Phys. B 20 010205
[4]	Tang Y N, Ma W X and Xu W 2012 Chin. Phys. B 21 070212
[5]	Wang H and Li B 2011 Chin. Phys. B 20 040203
[6]	Zuo J M and Zhang Y M 2011 Chin. Phys. B 20 010205
[7]	Zha Q L and Li Z B 2008 Chin. Phys. B 17 2333
[8]	Gilson C, Lambert F, Nimmo J and Willox R 1996 Proc. R. Soc. Lond. A 452 223
[9]	Lambert F and Springael J 2008 Acta. Appl. Math. 102 147
[10]	Fan E G 2011 Phys. Lett. A 375 493
[11]	Fan E G and Hou Y C 2011 J. Math. Phys. 52 023504
[12]	Fan E G 2011 Stud. Appl. Math. 127 284
[13]	Qin B, Tian B, Liu L C, Wang M, Lin Z Q and Liu W J 2011 J. Math. Phys. 52 043523
[14]	Wang Y F, Tian B, Wang P, Li M and Jiang Y 2012 Nonlinear Dyn. 69 2031
[15]	Zhang Y, Wei W W, Cheng T F and Song Y 2011 Chin. Phys. B 20 110204
[16]	Hu X R and Chen Y 2011 J. Nonlinear Math. Phys. 19 1
[17]	Wang Y H and Chen Y 2012 Commun. Theor. Phys. 57 217
[18]	Wang Y H and Chen Y 2012 J. Math. Phys. 53 123504
[19]	Lu X, Tian B and Qi F H 2012 Nonlinear Anal.: Real. 13 1130
[20]	Wazwaz A W 2010 Stud. Math. Sci. 1 21
[21]	Calogero F and Degasperis A 1976 Nuovo. Cimento. B 32 201
[22]	Bogoyavlenskii O I 1990 Russ. Math. Surveys 45 1
[23]	Lou S Y and Ruan H Y 2001 J. Phys. A: Math. Gen. 34 305
[24]	Zhang J F and Meng J P 2004 Phys. Lett. A 321 173
[25]	Geng X G and Cao C W 2004 Chaos. Soliton. Fract. 22 683
[26]	Wang D S and Li H B 2007 Appl. Math. Comput. 188 762
[27]	Ma W X, Zhou R G and Gao L 2009 Mod. Phys. Lett. A 24 1677
[28]	Hao H H, Zhang D J, Zhang J B and Yao Y Q 2010 Commun. Theor. Phys. 53 430
[29]	Cui K 2012 Chin. Phys. Lett. 29 060508
[30]	Chen Y, Li B and Zhang H Q 2003 Chin. Phys. 12 940
[31]	Fan E G and Hou Y C 2008 Phys. Rev. E 78 036607
[32]	Wadati M, Sanuki H and Konno K 1975 Prog. Theo. Phys. 53 419
[33]	Zhang D J and Chen D Y 2002 Chaos Soliton. Fract. 14 573
[34]	He G L and Geng X G 2012 Chin. Phys. B 21 070205
[35]	Konno K, Sanuki H and Ichikawa Y H 1974 Prog. Theo. Phys. 52 886
[36]	Zakharov V and Shabat A 1972 Sov. Phys. JETP 34 62
[37]	Tsuchida T and Wadati M 1998 J. Phys. Soc. Jpn. 67 1175
[38]	Kajiwara K, Matsukidaira J and Satsuma J 1990 Phys. Lett. A 146 1175
[39]	Bell E T 1934 Ann. Math. 35 258

[1]	Two integrable generalizations of WKI and FL equations: Positive and negative flows, and conservation laws Xian-Guo Geng(耿献国), Fei-Ying Guo(郭飞英), Yun-Yun Zhai(翟云云). Chin. Phys. B, 2020, 29(5): 050201.
[2]	An extension of integrable equations related to AKNS and WKI spectral problems and their reductions Xian-Guo Geng(耿献国), Yun-Yun Zhai(翟云云). Chin. Phys. B, 2018, 27(4): 040201.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Integrability of extended (2+1)-dimensional shallow water wave equation with Bell polynomials

Cite this article:

Online attention