Related papers: N=4 supersymmetric integrable systems

A general construction of integrable hierarchies based on affine Lie algebras is presented. The models are specified according to some algebraic data and their time evolution is obtained from solutions of the zero curvature condition. Such…

The first two Hamiltonian structures and the recursion operator connecting all evolution systems and Hamiltonian structures of the N=2 supersymmetric (n,m)-GNLS hierarchy are constructed in terms of N=2 superfields in two different…

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…

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 study the KdV and Burgers nonlinear systems and show in a consistent way that they can be mapped to each other through a strong requirement about their evolutions's flows to be connected. We expect that the established mapping between…

Three inequivalent real forms of the complex N=4 supersymmetric Toda chain hierarchy (Nucl. Phys. B558 (1999) 545, solv-int/9907004) in the real N=2 superspace with one even and two odd real coordinates are presented. It is demonstrated…

We construct $N=4$ supersymmetric KdV equation as a hamiltonian flow on the $N=4\;SU(2)$ super Virasoro algebra. The $N=4$ KdV superfield, the hamiltonian and the related Poisson structure are concisely formulated in $1D \;N=4$ harmonic…

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 give a brief account of two recent applications of the harmonic superspace method: (i) an off-shell description of torsionful $(4,4)$ supersymmetric $2D$ sigma models in the framework of $SU(2)\times SU(2)$ harmonic superspace and (ii)…

We obtain novel solutions of a coupled $\phi^4$, a coupled nonlinear Schr\"odinger (NLS) and a coupled modified Korteweg de Vries (MKdV) model which can be re-expressed as a linear superposition of either the sum or the difference of two…

For any two arbitrary positive integers `$n$' and `$m$', using the $m$--th KdV hierarchy and the $(n+m)$--th KdV hierarchy as building blocks, we are able to construct another integrable hierarchy (referred to as the $(n,m)$--th KdV…

We describe an infinite-dimensional algebra of hidden symmetries of N=4 supersymmetric Yang-Mills (SYM) theory. Our derivation is based on a generalization of the supertwistor correspondence. Using the latter, we construct an infinite…

Upon having presented a bird's eye view of history of integrable systems, we give a brief review of certain earlier advances (arXiv:1401.2122 & arXiv:1812.02263) in the longstanding problem of search for partial differential systems in four…

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…

The algebraic structure of the integrable mixed mKdV/sinh-Gordon model is discussed and \textit{}extended to the AKNS/Lund-Regge model and to its corresponding supersymmetric versions. The integrability of the models is guaranteed from the…

The quantization procedure for both N=1 and N=2 supersymmetric Korteweg-de Vries (SUSY KdV) hierarchies is constructed. Namely, the quantum counterparts of the monodromy matrices, built by means of the integrated vertex operators, are shown…

The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…

We continue the study of the quantization of supersymmetric integrable KdV hierarchies. We consider the N=2 KdV model based on the $sl^{(1)}(2|1)$ affine algebra but with a new algebraic construction for the L-operator, different from the…

A few 2+1-dimensional equations belonging to the KP and modified KP hierarchies are shown to be sufficient to provide a unified picture of all the integrable cases of the cubic and quartic H\'enon-Heiles Hamiltonians.

Two generalized Harry Dym equations, recently found by Brunelli, Das and Popowicz in the bosonic limit of new supersymmetric extensions of the Harry Dym hierarchy [J. Math. Phys. 44:4756--4767 (2003)], are transformed into previously known…