Differential equations extended to superspace

TL;DR

This paper extends classical differential equations into superspace using N=2 supersymmetry, resulting in coupled superfield equations, exemplified by the Riccati equation, to explore supersymmetric solutions.

Contribution

It introduces a straightforward method to embed differential equations into superspace with superfields, preserving original operators and coefficients, and applies it to the Riccati equation.

Findings

Derived coupled superfield equations for differential equations in superspace.

Provided a supersymmetric extension of the Riccati equation.

Established a self-consistent framework for superspace differential equations.

Abstract

We present a simple SUSY N=2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get selfconsistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution