In this paper, we review various properties of the supersymmetric Two-Boson (sTB) system.
We discuss the equation and its nonstandard Lax representation. We construct the local …

To our wives, Masha and Marian Interest in the so-called completely integrable systems with
infinite num ber of degrees of freedom was aroused immediately after publication of the …

We present the results of further analysis of the integrability properties of the N= 4
supersymmetric Korteweg–de Vries (KdV) equation deduced earlier by two of us [F. Delduc …

We give the formulation in extended superspace of an N= 2 supersymmetric KP hierarchy
using chirality preserving pseudo-differential operators. We obtain two quadratic hamiltonian …

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 …

This package deals with supersymmetric functions and with the algebra of supersymmetric
operators in extended N= 2 as well as in nonextended N= 1 supersymmetry. It allows us to …

We describe three different approaches to the extended (N= 2) supersymmetrization of the
multicomponent KP hierarchy. In the first one we utilize only superfermions while in the …

One can find in the literature many examples of supersymmetric hierarchies see, eg, Refs. 1–
7 but a general discussion of these hierarchies in the Drinfeld–Sokolov DS reduction …

We present a new integrable extension of the a=− 2, N= 2 SKdV hierarchy, with the “small”
N= 4 superconformal algebra (SCA) as the second hamiltonian structure. As distinct from the …

We construct a new variety of N= 2 supersymmetric integrable systems by the junction of
pseudo-differential superspace Lax operators for a= 4, N= 2 KdV and multi-component N= 2 …