Integrable System Constructed out of Two Interacting Superconformal Fields

TL;DR

This paper introduces a new integrable system based on interacting superconformal fields, providing a supersymmetric extension of classical equations and exploring its unique properties and reductions.

Contribution

It constructs a novel supersymmetric integrable system with a supersymmetric Poisson tensor and Lax representation, extending classical integrable models.

Findings

Developed a supersymmetric Poisson tensor for interacting superconformal fields.

Derived a Lax representation for the new supersymmetric equation.

Showed the system reduces to supersymmetric KdV in a specific limit, but with distinct integrals of motion.

Abstract

We describe how it is possible to introduce the interaction between superconformal fields of the same conformal dimensions. In the classical case such construction can be used to the construction of the Hirota - Satsuma equation. We construct supersymmetric Poisson tensor for such fields, which generates a new class of Hamiltonin systems. We found Lax representation for one of equation in this class by supersymmetrization Lax operator responsible for Hirota - Satsuma equation. Interestingly our supersymmetric equation is not reducible to classical Hirota - Satsuma equation. We show that our generalized system is reduced to the one of the supersymmetric KDV equation (a=4) but in this limit integrals of motion are not reduced to integrals of motion of the supersymmetric KdV equation.