Toward the construction of N=2 supersymmetric integrable hierarchies

Abstract

We formulate a conjecture for the three different Lax operators that describe the bosonic sectors of the three possible $N=2$ supersymmetric integrable hierarchies with $N=2$ super $W_n$ second hamiltonian structure. We check this conjecture in the simplest cases, then we verify it in general in one of the three possible supersymmetric extensions. To this end we construct the $N=2$ supersymmetric extensions of the Generalized Non-Linear Schrödinger hierarchy by exhibiting the corresponding super Lax operator. To find the correct hamiltonians we are led to a new definition of super-residues for degenerate N=2 supersymmetric pseudodifferential operators. We have found a new non-polinomial Miura-like realization for $N=2$ superconformal algebra in terms of two bosonic chiral--anti--chiral free superfields.

17 pages, Latex, a few more misprints have been corrected

References in corpus (3)

• THE MINIMAL N=2 SUPEREXTENSION OF THE NLS EQUATION
• On the Super-NLS Equation and its Relation with N=2 Super-KdV within Coset Approach
• The Extended Supersymmetrization of the Multicomponent Kadomtsev--Petviashvilli Hierarchy

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• Symmetries of Supersymmetric Integrable Hierarchies of KP Type
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• The Discrete Symmetry of the N=2 Supersymmetric Modified NLS Hierarchy
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• N=4 Sugawara construction on affine sl(2|1), sl(3) and mKdV-type superhierarchies
• Canonical gauge equivalences of the sAKNS and sTB hierarchies
• Supersymmetry at BLTP: how it started and where we are
• A note on the third family of N=2 supersymmetric KdV hierarchies
• Alternative dispersionless limit of N=2 supersymmetric KdV-type hierarchies
• Super-Affine Hierarchies and their Poisson Embeddings
• N=2 supersymmetric unconstrained matrix GNLS hierarchies are consistent
• N=4 supersymmetric integrable systems
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