N=2 supersymmetric unconstrained matrix GNLS hierarchies are consistent

TL;DR

This paper introduces a pseudo-differential approach to N=2 supersymmetric matrix hierarchies, proving their Lax pair consistency and equivalence to super-algebraic integrable hierarchies, with a novel definition of supersymmetric pseudo-differential operators.

Contribution

It develops a new pseudo-differential framework for N=2 supersymmetric hierarchies and establishes their consistency and equivalence to super-algebraic formulations.

Findings

Proved the Lax-pair representation is consistent.

Established equivalence to super-algebraic hierarchies.

Introduced a new definition of supersymmetric pseudo-differential operators.

Abstract

We develop a pseudo-differential approach to the N=2 supersymmetric unconstrained matrix (k|n,m)-Generalized Nonlinear Schroedinger hierarchies and prove consistency of the corresponding Lax-pair representation (nlin.SI/0201026). Furthermore, we establish their equivalence to the integrable hierarchies derived in the super-algebraic approach of the homogeneously-graded loop superalgebra sl(2k+n|2k+m)\otimes C[{lambda},{lambda}^{-1}] (nlin.SI/0206037). We introduce an unconventional definition of N=2 supersymmetric strictly pseudo-differential operators so as to close their algebra among themselves.