Gauge Equivalence, Supersymmetry and Classical Solutions of the ospu($1, 1/1$) Heisenberg Model and the Nonlinear Schr\"odinger Equation

TL;DR

This paper constructs an integrable superalgebra-based generalization of the classical Heisenberg model, establishes its gauge equivalence with the nonlinear Schrödinger equation, and introduces a method to generate solutions using supersymmetry.

Contribution

It introduces a novel integrable model based on ospu(1,1/1) superalgebra and links it to the NLSE, providing a new approach to generate classical solutions via supersymmetry.

Findings

Established gauge equivalence between the superalgebra model and NLSE.

Developed a method to generate solutions using supersymmetry.

Linked solutions of the classical Heisenberg model to superpartners of NLSE.

Abstract

An integrable generalization of the continuous classical O$(2,1)$ pseudospin Heisenberg model to the case of the ospu$(1,1/1)$ superalgebra is constructed. The gauge equivalence of the constructed model and the related NLSE is established. We indicate a method of generating classical solutions using the global ospu$(1,1/1)$ supersymmetry. The relationship between solutions of O$(2,1)$ HM and 'superpartners' of NLSE is obtained.