Grammian and Pfaffian solutions as well as Pfaffianization for a (3+1)-dimensional generalized shallow water equation

doi:10.1088/1674-1056/21/7/070212

Abstract Based on the Grammian and Pfaffian derivative formulae, Grammian and Pfaffian solutions are obtained for a (3+1)-dimensional generalized shallow water equation in the Hirota bilinear form. Moreover, a Pfaffian extension is made for the equation by means of the Pfaffianization procedure, the Wronski-type and Gramm-type Pfaffian solutions of the resulting coupled system are presented.

Keywords: Hirota bilinear form Grammian and Pfaffian solutions Wronski-type and Gramm-type Pfaffian solutions

Received: 21 November 2011
Revised: 05 January 2012
Accepted manuscript online:

PACS:	02.90.+p	(Other topics in mathematical methods in physics)
	02.30.Ik	(Integrable systems)
	05.45.Yv	(Solitons)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10932009 and 11172233), the Northwestern Polytechnical University Foundation for Fundamental Research, China (Grant No. GBKY1034), the State Administration of Foreign Experts Affairs of China, and the Chunhui Plan of the Ministry of Education of China.

Corresponding Authors: Tang Ya-Ning
E-mail: tyaning@nwpu.edu.cn

Cite this article:

Tang Ya-Ning(唐亚宁), Ma Wen-Xiu(马文秀), and Xu Wei(徐伟) Grammian and Pfaffian solutions as well as Pfaffianization for a (3+1)-dimensional generalized shallow water equation 2012 Chin. Phys. B 21 070212

[1]	Taogetusang 2011 Acta Phys. Sin. 60 070203 (in Chinese)
[2]	Yang Z, Ma S H and Fang J P 2011 Acta Phys. Sin. 60 040508 (in Chinese)
[3]	Su J, Xu W, Duan D H and Xu G J 2011 Acta Phys. Sin. 60 110203 (in Chinese)
[4]	Qian C, Wang L L and Zhang J F 2011 Acta Phys. Sin. 60 064214 (in Chinese)
[5]	Satsuma J 1979 J. Phys. Soc. Jpn. 46 359
[6]	Matveev V B 1992 Phys. Lett. A 166 200
[7]	Freeman N C and Nimmo J J C 1983 Phys. Lett. A 95 1
[8]	Nimmo J J C and Freeman N C 1983 Phys. Lett. A 95 4
[9]	Ma W X 2002 Phys. Lett. A 301 35
[10]	Ma W X and You Y C 2005 Trans. Amer. Math. Soc. 357 1753
[11]	Ma W X, Li C X and He J S 2009 Nonlinear Anal. 70 4245
[12]	Li C X, Ma W X, Liu X J and Zeng Y B 2007 Inverse Probl. 23 279
[13]	Geng X G and Ma Y L 2007 Phys. Lett. A 369 285
[14]	Wu J P 2011 Chin. Phys. Lett. 28 050501
[15]	Tang Y N, Ma W X, Xu W and Gao L 2011 Appl. Math. Comput. 217 8722
[16]	Hirota R 2004 The Direct Method in Soliton Theory (Cambridge: Cambridge University Press)
[17]	Wu J P and Geng X G 2009 Commun. Theor. Phys. 52 791
[18]	Ma W X, Abdeljabbar A and Asaad M G 2011 Appl. Math. Comput. 217 10016
[19]	Nakamura A 1989 J. Phys. Soc. Jpn. 58 412
[20]	Hirota R 1989 J. Phys. Soc. Jpn. 58 2285
[21]	Hietarinta J 2005 Phys. AUC 15 31
[22]	Tian B and Gao Y T 1996 Comput. Phys. Commu. 95 139
[23]	Zayed E M E 2010 J. Appl. Math. Informatics 28 383
[24]	Hirota R and Ohta Y 1991 J. Phys. Soc. Jpn. 60 798
[25]	Ma W X and Fan E G 2011 Comput. Math. Appl. 61 950

[1]	Lump-type solutions of a generalized Kadomtsev-Petviashvili equation in (3+1)-dimensions Xue-Ping Cheng(程雪苹), Wen-Xiu Ma(马文秀), Yun-Qing Yang(杨云青). Chin. Phys. B, 2019, 28(10): 100203.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Grammian and Pfaffian solutions as well as Pfaffianization for a (3+1)-dimensional generalized shallow water equation

Cite this article:

Online attention