中国物理B ›› 2018, Vol. 27 ›› Issue (4): 40203-040203.doi: 10.1088/1674-1056/27/4/040203
Constructing (2+1)-dimensional N=1 supersymmetric integrable systems from the Hirota formalism in the superspace
Jian-Yong Wang(王建勇), Xiao-Yan Tang(唐晓艳), Zu-Feng Liang(梁祖峰)
- 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
Constructing (2+1)-dimensional N=1 supersymmetric integrable systems from the Hirota formalism in the superspace
Jian-Yong Wang(王建勇)1, Xiao-Yan Tang(唐晓艳)2, Zu-Feng Liang(梁祖峰)3
- 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
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 (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.
中图分类号: (Partial differential equations)
- 02.30.Jr