N = 2 Supersymmetric Unconstrained Matrix GNLS Hierarchies are Consistent

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Abstract

We develop a pseudo-differential approach to the N = 2 supersymmetric unconstrained matrix (k|n, m)-generalized nonlinear Schrödinger 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)⊗C[λ, λ-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.

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