On the Super-NLS Equation and its Relation with N=2 Super-KdV within Coset Approach

TL;DR

This paper introduces an $N=2$ supersymmetric coset formalism to analyze the super-NLS equation, revealing its connection to the $a=4$ $N=2$ super-KdV hierarchy through a Bäcklund transformation, and constructs associated Lax pairs.

Contribution

It develops a manifest $N=2$ coset approach to integrable hierarchies and uncovers a novel Bäcklund transformation linking super-NLS and super-KdV equations.

Findings

Existence of a Bäcklund transformation connecting super-NLS and super-KdV.

Construction of $N=2$ scalar Lax pair operators for both equations.

Demonstration of $N=2$ symmetry in the super-NLS equation.

Abstract

A manifestly $N=2$ supersymmetric coset formalism is introduced to describe integrable hierarchies. It is applied to analyze the super-NLS equation. It possesses an $N=2$ symmetry since it can be obtained from a manifest $N=2$ coset algebra construction. A remarkable result is here discussed: the existence of a B\"{a}cklund transformation which connects the super-NLS equation to the equations belonging to the integrable hierarchy of one particular (the $a=4$) $N=2$ super-KdV equation. $N=2$ scalar Lax pair operators are introduced for both super-KdV and super-NLS.