Generalized Super Bell Polynomials with Applications to Superymmetric Equations

TL;DR

This paper introduces generalized super Bell polynomials as a new tool for analyzing supersymmetric equations, establishing their properties and applications in integrability, bilinear forms, Bäcklund transformations, Lax pairs, and conservation laws.

Contribution

It presents a novel class of super Bell polynomials and demonstrates their utility in systematically studying the integrability of supersymmetric equations.

Findings

Established connections between super Bell polynomials and supersymmetric integrability structures.

Applied the framework to supersymmetric KdV and sine-Gordon equations.

Showed that super Bell polynomials facilitate the derivation of bilinear forms and conservation laws.

Abstract

In this paper, we introduce a class of new generalized super Bell polynomials on a superspace, explore their properties, and show that they are a natural and effective tool to systematically investigate integrability of supersymmetric equations. The connections between the super Bell polynomials and super bilinear representation, bilinear B\"{a}cklund transformation, Lax pair and infinite conservation laws of supersymmetric equations are established. We take supersymmetric KdV equation and supersymmetric sine-Gordon equation to illustrate this procedure.