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

TL;DR

This paper introduces a bilinear Hirota representation for the N=2 supersymmetric KdV equation using binary Bell polynomials, and proposes a new generalization approach for the Hirota formalism in supersymmetric systems.

Contribution

It presents a novel bilinear Hirota representation for the N=2 supersymmetric KdV equation and introduces a new method for extending Hirota formalism to supersymmetric models.

Findings

Derived a Hirota bilinear form for N=2 supersymmetric KdV

Utilized binary Bell polynomials and hierarchies in the derivation

Proposed a new approach for supersymmetric Hirota formalism

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.