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

作　　者：Jian-Yong Wang Xiao-Yan Tang Zu-Feng Liang 王建勇;唐晓艳;梁祖峰(Department of Mathematics and Physics,Quzhou University;Shanghai Key Laboratory of Trustworthy Computing,East China Normal University;Department of Physics,Hangzhou Normal University)

机构地区：[1]Department of Mathematics and Physics, Quzhou University, Quzhou 324000, China [2]Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China [3]Department of Physics, Hangzhou Normal University, Hangzhou 310036, China

出　　处：《Chinese Physics B》2018年第4期144-153,共10页中国物理B（英文版）

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

摘　　要：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（MKd V） 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 MKd V 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.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（MKd V） 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 MKd V 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.

关 键 词：formal series symmetry approach generalized symmetry supersymmetric NKP system supersymmetric MKdV system 

分 类 号：O41[理学—理论物理]