新的(2+1)维超对称可积方程

数学物理学报 ›› 2020, Vol. 40 ›› Issue (5): 1132-1141.

新的(2+1)维超对称可积方程

陈芳^1,²,孙泽宇¹,陈敏茹³,颜昭雯^1,*()

¹ 内蒙古大学数学科学学院呼和浩特 010021
² 东北师范大学数学与统计学院长春 130024
³ 河南大学数学与信息科学学院河南开封 475001

收稿日期:2019-06-12 出版日期:2020-10-26 发布日期:2020-11-04
通讯作者: 颜昭雯 E-mail:yanzw@imu.edu.cn
基金资助:
国家自然科学基金(11965014);国家自然科学基金(11605096);国家自然科学基金(11505046);内蒙古大学自治区级大学生创新创业训练项目(201910126062)

The Novel (2+1)-Dimensional Supersymmetric Integrable Equations

Fang Chen^1,²,Zeyu Sun¹,Minru Chen³,Zhaowen Yan^1,*()

¹ School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021
² School of Mathematics and Statistics, Northeast Normal University, Changchun 130024
³ College of Mathematics and Information Sciences, Henan University, Henan Kaifeng 475001

Received:2019-06-12 Online:2020-10-26 Published:2020-11-04
Contact: Zhaowen Yan E-mail:yanzw@imu.edu.cn
Supported by:
the NSFC(11965014);the NSFC(11605096);the NSFC(11505046);the Autonomous Region forUndergraduate Innovation Training Program for Inner Mongolia University(201910126062)

摘要/Abstract

摘要：

该文基于超李代数osp（2/2），利用两种方法构造了新的（2+1）维超对称可积方程.一种方法是利用超李代数的齐性空间，另一种是增加系统维数的方法.此外，该文还导出了（2+1）维超对称可积方程的贝克隆变换.

关键词: 超对称可积方程, 超李代数, 贝克隆变换

Abstract:

Base on the super Lie algebra osp(2/2), we construct the (2+1)-dimensional supersymmetric integrable equations by means of two approaches. One of the technique is in terms of homogeneous spaces of super-Lie algebra, and in the other one, extending the dimension of the system has been used. Moreover, we derive the Bäcklund transformations for the (2+1)-dimensional supersymmetric integrable equations.

Key words: Supersymmetric integrable equations, Super Lie algebra, Bäcklund transformations

中图分类号:

陈芳,孙泽宇,陈敏茹,颜昭雯. 新的(2+1)维超对称可积方程[J]. 数学物理学报, 2020, 40(5): 1132-1141.

Fang Chen,Zeyu Sun,Minru Chen,Zhaowen Yan. The Novel (2+1)-Dimensional Supersymmetric Integrable Equations[J]. Acta mathematica scientia,Series A, 2020, 40(5): 1132-1141.

参考文献 30

1	Alvarez-Gaumé L , Itoyama H , Mañes J L , Zadra A . Superloop equations and two-dimensional supergravity. Int J Mod Phys A, 1992, 7, 5337- 5367 doi: 10.1142/S0217751X92002441
2	Wulff L . Integrability of the superstring in AdS3×S2×S2×T3. J Phys A, 2017, 50, 23L
3	Grabner D , Gromov N , Kazakov V , Korchemsky G . Strongly Gamma-deformed N=4 supersymmetric Yang-Mills theory as an integrable conformal field theory. Phys Rev Lett, 2018, 120, 111601 doi: 10.1103/PhysRevLett.120.111601
4	Hosomichi K , Lee S , Okuda T . Supersymmetric vortex defects in two dimensions. J High Energy Phys, 2018, 01, 033- 098
5	Di Vecchia P , Ferrara S . Classical solutions in two-dimensional supersymmetric field theories. Nucl Phys B, 1997, 130, 93- 104
6	Mathieu P . Supersymmetric extension of the korteweg-de vries. J Math Phys, 1988, 29, 2499- 2506 doi: 10.1063/1.528090
7	Bellucci S , Ivanov E , Krivonos S , Pichugin A . N=2 super boussinesq hierarchy:Lax pairs and conservation laws. Phys Lett B, 1993, 312, 463- 470 doi: 10.1016/0370-2693(93)90983-O
8	Manin Yu , Radul A . A supersymmetric extension of the Kadomtsev-Petviashvili hierarchy. Commun Math Phys, 1985, 98, 65- 77 doi: 10.1007/BF01211044
9	Kac V, Medina E. On the super-kp hierachy. Lett Math Phys, 1996, 37: 435-448
10	LeClair A . Supersymmetric KP hierarchy:free field construction. Nucl Phys B, 1989, 314, 425- 438 doi: 10.1016/0550-3213(89)90160-0
11	Popowicz Z . The extended supersymmetrization of the nonlinear schrödinger equation. Phys Lett A, 1994, 194, 375- 379 doi: 10.1016/0375-9601(94)91296-3
12	Mao H , Liu Q P . Bäcklund-Darbous transformations and discretizations of N=2 a=-2 supersymmetric KdV equation. Phys Lett A, 2018, 382, 253- 258 doi: 10.1016/j.physleta.2017.11.034
13	Aguirre A R , Retore A L , Gomes J F , et al. Defects in the supersymmetric MKdV hierarchy via Bäcklund transformations. J High Energy Phys, 2018, 01, 018
14	Chaichian M , Kulish P P . On the method of inverse scattering problem and Bäcklund transformation for supersymmetric equations. Phys Lett B, 1978, 78, 413- 416 doi: 10.1016/0370-2693(78)90473-2
15	Mathieu P . The painlevé property for fermionic extensions of the Korteweg-de Vries equation. Phys Lett A, 1988, 128, 169- 171 doi: 10.1016/0375-9601(88)90903-6
16	Ibort A , Martinez Alonso L , Medina Reus E . Explicit solutions of supersymmetric KP hierarchies:supersolitinos. J Math Phys, 1996, 37, 6157- 6172 doi: 10.1063/1.531770
17	Liu Q P . Darbous transformations for supersymmetric Korteweg-de Vries equations. Lett Math Phys, 1995, 35, 115- 122 doi: 10.1007/BF00750761
18	McArthur I N , Yung C M . Hirota bilinear from for the super-KdV hierarchy. Mod Phys Lett A, 1993, 8, 1739- 1745 doi: 10.1142/S0217732393001471
19	Wahlquist H D , Estabrook F B . Prolongation structures of nonlinear evolution equations. J Math Phys, 1975, 16, 1- 7 doi: 10.1063/1.522396
20	Saha M , Roy Chowdhury A . Supersymmetric integrable systems in (2+1) dimensional and their Bäcklund transformation. Int J Theor Phys, 1999, 38, 2037- 2047 doi: 10.1023/A:1026605819631
21	Yan Z W , Chen M R , Wu K , Zhao W Z . (2+1)-dimensional integrable Heisenberg supermagnet model. J Phys Soc Jpn, 2012, 81, 094006 doi: 10.1143/JPSJ.81.094006
22	Cheng J P , Tian Y , Yan Z W , He J S . The generalized additional symmetries of the two-Toda lattice hierarchy. J Math Phys, 2013, 54, 023513 doi: 10.1063/1.4792479
23	Yan Z W , Li M L , Wu K , Zhao W Z . Fermionic covariant prolongation structure theory for multidimensional super nonlinear evolution equation. J Math Phys, 2013, 54, 033506 doi: 10.1063/1.4795405
24	Hu X B . An approach to generate superextensions of integrable systems. J Phys A, 1997, 30, 619- 632 doi: 10.1088/0305-4470/30/2/023
25	Suh U R . Classical affine w-superalgebras via generalized Drinfeld-Sokolov reductions and related integrable systems. Commun Math Phys, 2018, 358, 199- 236 doi: 10.1007/s00220-017-3014-7
26	Berkovits N , Vafa C , Witten E . Conformal field theory of AdS background with Ramond-Radmond flux. J High Energy Phys, 1999, 03, 018
27	Gurarie V . Logarithmic operators in conformal field theory. Nucl Phys B, 1993, 410, 535- 549 doi: 10.1016/0550-3213(93)90528-W
28	Guruswamy S , LeClair A , Ludwig A W W . gl(N\|N) super-current algebras for disordered Dirac fermions in two dimensions. Nucl Phys B, 2000, 583, 475- 512 doi: 10.1016/S0550-3213(00)00245-5
29	Yin Z , Yu L , Li M L . On a supersymmetric nonlinear integrable equation in (2+1) dimensions. J Nonlin Math Phys, 2015, 22, 204- 209 doi: 10.1080/14029251.2015.1023581
30	Yan Z W , Chen F T , Liu T R , Han J M . (2+1)-dimensional supersymmetric integrable equations. Int J Geom Methods M, 2017, 14, 1750013 doi: 10.1142/S021988781750013X

[1]	郭秀荣, 胡美燕. 两个可积系统及其约化[J]. 数学物理学报, 2014, 34(5): 1304-1312.
[2]	曹锡芳, 徐传友. 常挠率运动曲线生成曲面上的贝克隆变换[J]. 数学物理学报, 2014, 34(1): 115-125.