Constructing (2+1)-dimensional N=1 supersymmetric integrable systems from the Hirota formalism in the superspace

doi:10.1088/1674-1056/27/4/040203

Abstract The N=1 supersymmetric extensions of two integrable systems, a special negative Kadomtsev-Petviashvili (NKP) system and a (2+1)-dimensional modified Korteweg-de Vries (MKdV) system, are constructed from the Hirota formalism in the superspace. The integrability of both systems in the sense of possessing infinitely many generalized symmetries are confirmed by extending the formal series symmetry approach to the supersymmetric framework. It is found that both systems admit a generalization of W_∞ type algebra and a Kac-Moody-Virasoro type subalgebra. Interestingly, the first one of the positive flow of the supersymmetric NKP system is another N=1 supersymmetric extension of the (2+1)-dimensional MKdV system. Based on our work, a hypothesis is put forward on a series of (2+1)-dimensional supersymmetric integrable systems. It is hoped that our work may develop a straightforward way to obtain supersymmetric integrable systems in high dimensions.

Keywords: formal series symmetry approach generalized symmetry supersymmetric NKP system supersymmetric MKdV system

Received: 23 December 2017
Revised: 15 January 2018
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	11.30.Pb	(Supersymmetry)
	02.20.Sv	(Lie algebras of Lie groups)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11605102, 11475052, 11675055, and 11626140).

Corresponding Authors: Jian-Yong Wang
E-mail: jywangqz@126.com

Cite this article:

Jian-Yong Wang(王建勇), Xiao-Yan Tang(唐晓艳), Zu-Feng Liang(梁祖峰) Constructing (2+1)-dimensional N=1 supersymmetric integrable systems from the Hirota formalism in the superspace 2018 Chin. Phys. B 27 040203

[1]	Di Vecchia P and Ferrara S 1977 Nucl. Phys. B 130 93
[2]	Mathieu P 1988 J. Math. Phys. 29 2499
[3]	Manin Yu I and Radul A O 1985 Commun. Math. Phys. 98 65
[4]	Delisle L and Mosaddeghi M 2013 J. Phys. A:Math. Theor. 46 115203
[5]	Wang J Y, Tang X Y, Liang Z F and Lou S Y 2015 Chin. Phys. B 24 050202
[6]	Henneaux M and Rey S J 2010 J. High Energy Phys. 12 007
[7]	Lou S Y 1993 J. Phys. A:Math. Gen. 26 4387
[8]	Ghosh S and Paul S K 1995 Phys. Lett. B 341 293
[9]	Lou S Y 1994 J. Phys. A:Math. Gen. 27 3235
[10]	Lou S Y 1994 J. Phys. A: Math. Gen. 27 3235
[11]	Lou S Y 1998 Phys. Scr. 57 481
[12]	Gegenhasi, Hu X B and Wang H Y 2007 Phys. Lett. A 360 439
[13]	Fan E G 2011 Stud. Appl. Math. 127 284
[14]	Jia M, Li J H and Lou S Y 2008 J. Phys. A:Math. Theor. 41 275204
[15]	Ito M 1980 J. Phys. Soc. Jpn. 49 771
[16]	Hietarinta J 1987 J. Math. Phys. 28 2094
[17]	Li J H and Lou S Y 2008 Chin. Phys. B 17 747
[18]	Peng L Z, Zhang M X, Gegenhasi and Liu Q P 2008 Phys. Lett. A 372 4197
[19]	Hietarinta J 1987 J. Math. Phys. 28 1732
[20]	Hietarinta J 1987 J. Math. Phys. 28 2586
[21]	Hietarinta J 1988 J. Math. Phys. 29 628
[22]	Sarma D 2004 Nucl. Phys. B 681 351
[23]	Liu Q P and Yang X X 2006 Phys. Lett. A 351 131
[24]	Fan E G and Hon Y C 2012 J. Math. Phys. 53 013503
[25]	Xue L L and Liu Q P 2013 Phys. Lett. A 377 828
[26]	Brunelli J C and Das A 1994 Phys. Lett. B 337 303
[27]	Wang J Y, Liang Z F and Tang X Y 2014 Phys. Scr. 89 025201
[28]	Tang X Y, Li J, Liang Z F and Wang J Y 2014 Phys. Lett. A 378 1439
[29]	Wang J Y, Yu J and Lou S Y 2010 Commun. Theor. Phys. 53 999
[30]	Wang J Y, Hu H W and Yu J 2011 J. Math. Phys. 52 103704

[1]	Generalized symmetries of an N=1 supersymmetric Boiti–Leon–Manna–Pempinelli system Wang Jian-Yong (王建勇), Tang Xiao-Yan (唐晓艳), Liang Zu-Feng (梁祖峰), Lou Sen-Yue (楼森岳). Chin. Phys. B, 2015, 24(5): 050202.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Constructing (2+1)-dimensional N=1 supersymmetric integrable systems from the Hirota formalism in the superspace

Cite this article:

Online attention