A N=2 extension of the Hirota bilinear formalism and the supersymmetric KdV equation

Abstract

We present a bilinear Hirota representation of the N=2 supersymmetric extension of the Korteweg-de Vries equation. This representation is deduced using binary Bell polynomials, hierarchies and fermionic limits. We, also, propose a new approach for the generalisation of the Hirota bilinear formalism in the N=2 supersymmetric context.