# The N=2 supersymmetric unconstrained matrix GNLS hierarchies

A.S. Sorin, P.H.M. Kersten

Research output: Book/ReportReportOther research output

4 Citations (Scopus)

## Abstract

The generalization of the $N=2$ supersymmetric chiral matrix $(k|n,m)$--GNLS hierarchy 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. The simplest example --- the $N=2$ unconstrained $(1|1,0)$--GNLS hierarchy --- and its reduction to the $N=2$ supersymmetric ${\alpha}=1$ KdV hierarchy are discussed in more detail, and its rich symmetry structure is uncovered.
Original language English Enschede University of Twente, Department of Applied Mathematics 11 Published - 2002

### Publication series

Name Memorandum Department of Applied Mathematics, University of Twente 1613 0169-2690

## Keywords

• MSC-35Q51
• MSC-35Q53
• IR-65800
• EWI-3433
• MSC-35Q58
• Completely integrable systems
• Discrete symmetries
• Supersymmetry

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