Related papers: N=4 Super NLS-mKdV Hierarchies
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 previously known N=4 supersymmetric KdV hierarchy associated…
The local Sugawara constructions of the "small" N=4 SCA in terms of supercurrents of N=2 extensions of the affinization of the sl(2|1) and sl(3) algebras are investigated. The associated super mKdV type hierarchies induced by N=4 SKdV ones…
We construct a new variety of $N=2$ supersymmetric integrable systems by junction of pseudo-differential superspace Lax operators for $a=4$, $N=2$ KdV and multi-component $N=2$ NLS hierarchies. As an important particular case, we obtain Lax…
We present the results of further analysis of the integrability properties of the $N=4$ supersymmetric KdV equation deduced earlier by two of us (F.D. \& E.I.) as a hamiltonian flow on $N=4$ $SU(2)$ superconformal algebra in the harmonic…
The N=2 supersymmetric {\alpha}=1 KdV hierarchy in N=2 superspace is considered and its rich symmetry structure is uncovered. New nonpolynomial and nonlocal, bosonic and fermionic symmetries and Hamiltonians, bi-Hamiltonian structure as…
We show that the well known $N=1$ NLS equation possesses $N=2$ supersymmetry and thus it is actually the $N=2$ NLS equation. This supersymmetry is hidden in terms of the commonly used $N=1$ superfields but it becomes manifest after passing…
We construct the $N=2$ super $W_4$ algebra as a certain reduction of the second Gel'fand-Dikii bracket on the dual of the Lie superalgebra of $N=1$ super pseudo-differential operators. The algebra is put in manifestly $N=2$ supersymmetric…
Integrable models with higher N=2 and N=4 supersymmetries are formulated on reductions of twisted loop superalgebras $\hat{sl}(2|2)$ and $\hat{sl}(4|4) $ endowed with principal gradation. In case of the $\hat{sl}(4|4)$ loop algebra a…
We point out that the N=4 supersymmetric KdV hierarchy, when written through the prepotentials of the bosonic chiral and antichiral N=2 supercurrents, exhibits a freedom related to the possibility to choose different gauges for the…
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 structures, which lead to different reductions of the KP…
A manifestly N=2 supersymmetric coset formalism is applied to analyse the "fermionic" extensions of N=2 $a=4$ and $a=-2$ KdV hierarchies. Both these hierarchies can be obtained from a manifest N=2 coset construction. This coset is defined…
We preesent a new supersymmetric integrable extensions of the a=4,N=2 KdV hierarchy. The root of the supersymmetric Lax operator of the KdV equation is generalized, by including additional fields. This generalized root generate new…
I give an overview of recent progress in constructing the KdV, mKdV and NLS type hierarchies with extended N=4 supersymmetry.
A new Lax operator is proposed from the viewpoint of constructing the integrable hierarchies related with N=2 super $W_n$ algebra. It is shown that the Poisson algebra associated to the second Hamiltonian structure for the resulted…
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…
We discuss a large class of coset constructions of the N=2 sl(n|n-1) affine superalgebra. We select admissible subalgebras, i.e. subalgebras that induce linear chiral/antichiral constraints on the coset supercurrents. We show that all the…
A few new N=2 superintegrable mappings in the (1|2) superspace are proposed and their origin is analyzed. Using one of them, acting like the discrete symmetry transformation of the N=2 supersymmetric modified NLS hierarchy, the recursion…
Lax pair and Hamiltonian formulations of the N=4 supersymmetric Toda chain (KdV) hierarchy in N=4 superspace are proposed. The general formulae for the infinite tower of its bosonic flows in terms of the Lax operator in N=4 superspace are…
A manifestly $N=2$ supersymmetric coset formalism is introduced to describe integrable hierarchies. It is applied to analyze the super-NLS equation. It possesses an $N=2$ symmetry since it can be obtained from a manifest $N=2$ coset algebra…
We construct N=2 affine current algebras for the superalgebras sl(n|n-1)^{(1)} in terms of N=2 supercurrents subjected to nonlinear constraints and discuss the general procedure of the hamiltonian reduction in N=2 superspace at the…