The Extended Supersymmetrization of the Nonlinear Schrodinger Equation

TL;DR

This paper introduces a new extended supersymmetric version of the nonlinear Schrödinger equation, incorporating two superboson fields with different gradations, and proves its integrability via a Lax formulation.

Contribution

It presents a novel extended supersymmetrization of the nonlinear Schrödinger equation with two superboson fields, differing from previous models, and establishes its integrability.

Findings

Model is integrable, confirmed by Lax formulation.

Different from previous supersymmetric models by Toppan, Kulish, Roelofs, and Kersten.

Introduces two superboson fields with distinct gradations.

Abstract

We present the new extended supersymmetrization of the Nonlinear Schrodinger Equation by introducing two superbosons fields with the different gradation. Our model is different from this considered by Toppan and in the reduced case (nonextended supersymmetry) is also different from this considered by Kulish and Roelofs and Kersten. We prove that our model is integrable by presenting its Lax formulation.