New non-local SUSY KdV conservation laws from a recursive gradient algorithm

TL;DR

This paper rigorously proves a recursive gradient method to construct all hierarchy structures, including non-local conserved quantities, for N=1 Super KdV, enriching the understanding of its integrability.

Contribution

It introduces a complete proof of the recursive gradient approach for N=1 Super KdV, including the construction of non-local conservation laws and defining the relevant superfield ring.

Findings

New non-local conserved quantities of N=1 Super KdV identified

Recursive gradient approach validated for hierarchy construction

Explicit ring of superfields for non-local structures defined

Abstract

A complete proof of the recursive gradient approach is presented. It gives a construction of all the hierarchy structures of N=1 Super KdV, including the non-local one. A precise definition of the ring of superfields involved in the non-local construction is given. In particular, new non-local conserved quantities of N=1 Super KdV are found.