A new (2+1)-dimensional supersymmetric Boussinesq equation and its Lie symmetry study

doi:10.1088/1674-1056/19/5/050202

Abstract According to the conjecture based on some known facts of integrable models, a new (2+1)-dimensional supersymmetric integrable bilinear system is proposed. The model is not only the extension of the known (2+1)-dimensional negative Kadomtsev--Petviashvili equation but also the extension of the known (1+1)-dimensional supersymmetric Boussinesq equation. The infinite dimensional Kac--Moody--Virasoro symmetries and the related symmetry reductions of the model are obtained. Furthermore, the traveling wave solutions including soliton solutions are explicitly presented.

Keywords: integrable models supersymmetry symmetries and symmetry reductions exact solutions

Received: 27 July 2009
Revised: 23 November 2009
Accepted manuscript online:

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

Fund: Project supported by the National Natural Science Foundation of China (Grant No.~10735030), the Scientific Research Fund of Zhejiang Provincial Education Department (Grant No.~20040969), the National Basic Research Programs of China (Grant Nos.~2007CB814800 and 2005CB422301) and the PCSIRT (IRT0734).

Cite this article:

Wang You-Fa(王友法), Lou Sen-Yue(楼森岳), and Qian Xian-Min(钱贤民) A new (2+1)-dimensional supersymmetric Boussinesq equation and its Lie symmetry study 2010 Chin. Phys. B 19 050202

[1]	Chavanis P H and Sommeria J 1997 Phys. Rev. Lett. 78 3302
[1a]	Chavanis P H 2000 Phys. Rev. Lett. 84 5512
[2]	Dolan L 1997 Nucl. Phys. B 489 245
[2a]	Distler J and Hanany A 1997 Nucl. Phys. B 496 75
[3]	Loutsenko I and Roubtsov D 1997 Phys. Rev. Lett. 78 3011
[3a]	Busch T and Anglin J R 2001 Phys. Rev. Lett. 87 010401
[3b]	Yang R S,Yao C M and Chen R X 2009 Chin. Phys. B 18 3736
[4]	Gedalin M, Scott T C and Band Y B 1997 Phys. Rev. Lett. 78 448
[4a]	Georges T 1997 Optics Lett. 22 679
[4b]	Tang Y and Yan X H 2000 Chin. Phys. 9 565
[5]	Weigel H, Gamberg L and Reinhardt H 1997 Phys. Rev. D 55 6919
[6]	Drinfeld V G and Sokolov V V Dokl 1981 Akal. Nauk. USSR 258 11
[7]	Wilson G 1981 Ergod Th Dynam. Syst. 1 361
[8]	Calogero F and Eckhaus W 1988 Inv. Prob. 3 229
[8a]	Calogero F, Degasperis A and Ji X D 2000 J. Math. Phys. 41 6399
[8b]	Calogero F, Degasperis A and Ji X D 2001 J. Math. Phys. 42 2635
[9]	Maccari A 1996 J. Math. Phys. 37 6207
[9a]	Maccari A 1998 Int. J. Nonlinear Mech. 33 713
[9b]	Maccari A 1998 Nonlinear Dynamics 15 329
[10]	Lou S Y 1997 Sci. China A40 1317
[11]	Lin J 1996 Commun. Theor. Phys. (Beijing, China) 25 447
[11a]	Lou S Y, Lin J and Yu J 1995 Phys. Lett. A201 47
[11b]	Lin J, Lou S Y and Wang K L 2000 Z. Naturforsch 55a 589
[12]	Yu J and Lou S Y 2000 Sci. China A 43 655
[12a]	Lou S Y, Yu J and Tang X Y 2000 Z. Naturforsch 55a 867
[13]	Lou S Y 1998 Phys. Rev. Lett. 80 5027
[13a]	Lou S Y 1998 J. Math. Phys. 39 2112
[13b]	Lou S Y and Xu J J 1998 Math. Phys. 80 5364
[13c]	Lou S Y 1997 Commun. Theor. Phys. (Beijing, China) 27 249
[14]	Li J H and Lou S Y 2008 Chin. Phys. B 17 747
[15]	Gegenhasi, Hu X B and Wang H Y 2007 Phys. Lett. A 360 439
[16]	Li J H, Jia M and Lou S Y 2007 J. Phys. A: Math. Theor. 40 1585
[17]	Liu Q P and Hu X B 2005 J. Phys. A 18 6371
[18]	Liu Q P, Hu X B and Zhang M X 2005 Nonlinearity 18 1597
[19]	Zhang M X, Liu Q P, Wang J and Wu K 2008 Chin. Phys. B 17 10
[20]	Liu Q P and Yang X X 2006 Phys. Lett. 351 131
[21]	Lou S Y 1998 Phys. Scr. 57 481
[22]	Guo C H, Li Y S, Cao C W, Tian C, Tu G Z, Hu H C, Guo B Y and Ge M L, 1990 Soliton Theory and its Application (Hangzhou, China: Zhejiang Publishing House of Science and Technology) p237
[23]	Olver P J 1986 Applications of Lie Group to Differential Equations (Berlin: Springer) p76
[24]	Mikhailov A V, Shabat A B and Sokolov V V 1991 What is Integrability (Berlin: Springer) p115
[25]	Lou S Y 2000 J. Math. Phys. 41 6509
[26]	Tang X Y and Shukla P K 2007 Phys. Scr. 76 665
[27]	Qian S P and Tian L X 2007 Chin. Phys. 16 303
[28]	Fan E G 2007 Chin. Phys. 16 1505
[29]	Ruan H Y and Chen Y X 2001 Chin. Phys. 10 87

[1]	Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions Fa-Kai Wen(温发楷) and Xin Zhang(张鑫). Chin. Phys. B, 2021, 30(5): 050201.
[2]	Supersymmetric structures of Dirac oscillators in commutative and noncommutative spaces Jing-Ying Wei(魏静莹), Qing Wang(王青), and Jian Jing(荆坚). Chin. Phys. B, 2021, 30(11): 110307.
[3]	Exact scattering states in one-dimensional Hermitian and non-Hermitian potentials Ruo-Lin Chai(柴若霖), Qiong-Tao Xie(谢琼涛), Xiao-Liang Liu(刘小良). Chin. Phys. B, 2020, 29(9): 090301.
[4]	Exact solution of the (1+2)-dimensional generalized Kemmer oscillator in the cosmic string background with the magnetic field Yi Yang(杨毅), Shao-Hong Cai(蔡绍洪), Zheng-Wen Long(隆正文), Hao Chen(陈浩), Chao-Yun Long(龙超云). Chin. Phys. B, 2020, 29(7): 070302.
[5]	Unified approach to various quantum Rabi models witharbitrary parameters Xiao-Fei Dong(董晓菲), You-Fei Xie(谢幼飞), Qing-Hu Chen(陈庆虎). Chin. Phys. B, 2020, 29(2): 020302.
[6]	Linear optical approach to supersymmetric dynamics Yong-Tao Zhan(詹颙涛), Xiao-Ye Xu(许小冶), Qin-Qin Wang(王琴琴), Wei-Wei Pan(潘维韦), Munsif Jan, Fu-Ming Chang(常弗鸣), Kai Sun(孙凯), Jin-Shi Xu(许金时), Yong-Jian Han(韩永建), Chuan-Feng Li(李传锋), Guang-Can Guo(郭光灿). Chin. Phys. B, 2020, 29(1): 014209.
[7]	Bright and dark soliton solutions for some nonlinear fractional differential equations Ozkan Guner, Ahmet Bekir. Chin. Phys. B, 2016, 25(3): 030203.
[8]	Application of asymptotic iteration method to a deformed well problem Hakan Ciftci, H F Kisoglu. Chin. Phys. B, 2016, 25(3): 030201.
[9]	Fusion, fission, and annihilation of complex waves for the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff system Zhu Wei-Ting (朱维婷), Ma Song-Hua (马松华), Fang Jian-Ping (方建平), Ma Zheng-Yi (马正义), Zhu Hai-Ping (朱海平). Chin. Phys. B, 2014, 23(6): 060505.
[10]	Oscillating multidromion excitations in higher-dimensional nonlinear lattice with intersite and external on-site potentials using symbolic computation B. Srividya, L. Kavitha, R. Ravichandran, D. Gopi. Chin. Phys. B, 2014, 23(1): 010307.
[11]	The nonrelativistic oscillator strength of a hyperbolic-type potential H. Hassanabadi, S. Zarrinkamar, B. H. Yazarloo. Chin. Phys. B, 2013, 22(6): 060202.
[12]	The Yukawa potential in semirelativistic formulation via supersymmetry quantum mechanics S. Hassanabadi, M. Ghominejad, S. Zarrinkamar, H. Hassanabadi. Chin. Phys. B, 2013, 22(6): 060303.
[13]	New exact solutions of (3+1)-dimensional Jimbo-Miwa system Chen Yuan-Ming (陈元明), Ma Song-Hua (马松华), Ma Zheng-Yi (马正义). Chin. Phys. B, 2013, 22(5): 050510.
[14]	Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations Liu Ping (刘萍), Li Zi-Liang (李子良). Chin. Phys. B, 2013, 22(5): 050204.
[15]	Comparative study of travelling wave and numerical solutions for the coupled short pulse (CSP) equation Vikas Kumar, R. K. Gupta, Ram Jiwari. Chin. Phys. B, 2013, 22(5): 050201.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

A new (2+1)-dimensional supersymmetric Boussinesq equation and its Lie symmetry study

Cite this article:

Online attention