Constructing (2+1)-dimensional supersymmetric integrable systems from the Hirota formalism in the superspace**Project supported by the National Natural Science Foundation of China (Grant Nos. 11605102, 11475052, 11675055, and 11626140).

Abstract

The 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 type algebra and a Kac-Moody–Virasoro type subalgebra. Interestingly, the first one of the positive flow of the supersymmetric NKP system is another 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.