N=2 supersymmetric unconstrained matrix GNLS hierarchies are consistent

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.

12 pages, LaTex

References in corpus (6)

• Toward the construction of N=2 supersymmetric integrable hierarchies
• The Extended Supersymmetrization of the Multicomponent Kadomtsev--Petviashvilli Hierarchy
• The Hamiltonian structure of the N=2 supersymmetric GNLS hierarchy
• Bi-Hamiltonian structure of the N=2 supersymmetric α=1 KdV hierarchy
• Supersymmetry for integrable hierarchies on loop superalgebras
• Coset approach to the N=2 supersymmetric matrix GNLS hierarchies