Constructing (2+1)-dimensional N =1 supersymmetric integrable systems from the Hirota formalism in the superspace
Constructing (2+1)-dimensional N =1 supersymmetric integrable systems from the Hirota formalism in the superspace
复制标题
从超空间中的 Hirota 形式构造 (2 1) 维 N =1 超对称可积系统
DOI：
10.1088/1674-1056/27/4/040203
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发表时间：
2018
影响因子：
1.7
通讯作者：
梁祖峰
中科院分区：
文献类型：
--
作者：
王建勇;唐晓艳;梁祖峰
利用超空间中的Hirota形式构造了两个可积系统的N=1超对称扩张：一个特殊的负Kadomtsev-Petviashvili(NKP)系统和一个(2+1)维修正的Korteweg-de Vries(MKdV)系统.通过将形式级数对称方法推广到超对称框架，证明了这两个系统在具有无穷多个广义对称意义下的可积性。结果表明，这两个系统都有一个推广的W-∞型代数和一个Kac-Moody-Virasoro子代数。有趣的是，超对称NKP系统的第一个正流是(2+1)维MKdV系统的另一个N=1超对称扩张。在我们工作的基础上，提出了关于(2+1)维超对称可积系统的一个假设。希望我们的工作能发展出一种直接获得高维超对称可积系统的方法。
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.(paper)