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The N=2 supersymmetric unconstrained matrix GNLS hierarchies

A. S. Sorin·P. H. M. Kersten
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Abstract

The generalization of the N=2 supersymmetric chiral matrix (k|n,m)--GNLS hierarchy (Lett. Math. Phys. 45 (1998) 63, solv-int/9711009) to the case when matrix entries are bosonic and fermionic unconstrained N=2 superfields is proposed. This is done by exhibiting the corresponding matrix Lax--pair representation in terms of N=2 unconstrained superfields. It is demonstrated that when matrix entries are chiral and antichiral N=2 superfields, it reproduces the N=2 chiral matrix (k|n,m)-GNLS hierarchy, while in the scalar case, k=1, it is equivalent to the N=2 supersymmetric multicomponent hierarchy (J. Phys. A29 (1996) 1281, hep-th/9510185). The simplest example --the N=2 unconstrained (1|1,0)--GNLS hierarchy-- and its reduction to the N=2 supersymmetric α=1 KdV hierarchy are discussed in more detail, and its rich symmetry structure is uncovered.

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A. S. Sorin, P. H. M. Kersten. 2002-01-20. The N=2 supersymmetric unconstrained matrix GNLS hierarchies. https://arxiv.org/abs/nlin/0201026

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