The quantum SKdV$_{1,4}$ equation at $c=3$

TL;DR

This paper investigates the quantum SKdV$_{1,4}$ equations at central charge c=3, revealing their equivalence and providing a simple proof of integrability through closed-form conservation laws.

Contribution

It demonstrates the equivalence of two quantum supersymmetric KdV equations at c=3 and presents a constructive proof of their integrability via closed-form conservation laws.

Findings

SKdV$_1$ and SKdV$_4$ are identical at c=3

All conservation laws can be expressed in closed form

Provides a straightforward proof of integrability

Abstract

At $c=3$, two of the three integrable quantum $N=2$ supersymmetric Korteweg-de Vries equations become identical (SKdV$_1$ and SKdV$_4$). Quite remarkably, all their conservation laws can be written in closed form, which provides thus a simple constructive integrability proof.