N=2 supersymmetric unconstrained matrix GNLS hierarchies are consistent

Details N=2 supersymmetric unconstrained matrix GNLS hierarchies are consistent N=2 supersymmetric unconstrained matrix GNLS hierarchies are consistent

2007-08-08

arxiv.org/abs/0708.1125v1

Lett.Math.Phys.84:109-122,2008

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, LaTex

Scientific paper

10.1007/s11005-008-0237-8

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.

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