Related papers: N=4 supersymmetric integrable systems
A systematic method of constructing manifestly supersymmetric $1+1$-dimensional KP Lax hierarchies is presented. Closed expressions for the Lax operators in terms of superfield eigenfunctions are obtained. All hierarchy equations being…
We construct in detail an N=1, D=4 superspace with the superconformal algebra as the structure group and discuss its relation to prior component approaches and the existing Poincar\'e superspaces.
A new type of high-dimensional Lie superalgebras is constructed, including Lie superalgebras spo(4,2) and osp(4,2). Based on it, two different coupled nonisospectral super AKNS hierarchies and their bi-Hamiltonian structures are obtained.…
A super-algebraic formulation of the N=2 supersymmetric unconstrained matrix (k|n,m)-MGNLS hierarchies (nlin.SI/0201026) is established. Recursion operators, fermionic and bosonic symmetries as well as their superalgebra are constructed for…
We discuss a differential integrable hierarchy, which we call the (N, M)$--th KdV hierarchy, whose Lax operator is obtained by properly adding $M$ pseudo--differential terms to the Lax operator of the N--th KdV hierarchy. This new hierarchy…
The first example of an N=8 supersymmetric extension of the KdV equation is here explicitly constructed. It involves 8 bosonic and 8 fermionic fields. It corresponds to the unique N=8 solution based on a generalized hamiltonian dynamics…
A N=4 supersymmetric matrix KP hierarchy is proposed and a wide class of its reductions which are characterized by a finite number of fields are described. This class includes the one-dimensional reduction of the two-dimensional N=(2|2)…
We introduce integrable KdV type hierarchy associated naturally with arbitrary semi-simple Frobenius manifold. We present hierarchy in a Lax form and show that it admits bihamiltonian description.
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.
We review the calculation and properties of the supersymmetric index for four dimensional N=1 theories, illustrating its physical significance in several examples.
We construct integrable and superintegrable Hamiltonian systems using the realizations of four dimensional real Lie algebras as a symmetry of the system with the phase space R4 and R6. Furthermore, we construct some integrable and…
We propose a consistently algebraic formulation of the extended KP (supersymmetric) integrable -hierarchy systems. We exploit the results already established in [14] and which consist in a framework suspected to unify in a fascinating way…
On a complex manifold $(M,J)$, we interpret complex symplectic and pseudo-K\"ahler structures as symplectic forms with respect to which $J$ is, respectively, symmetric and skew-symmetric. We classify complex symplectic structures on…
The purpose of this paper is to express the entire hierarchy of mKdV vector fields as restrictions of vector fields in the NLS hierarchy. The result is proved using the normal form theory of the two equations.
Following our previous works on extended higher spin symmetries on the torus we focus in the present contribution to make a setup of the integrable KdV hierarchies on $T^{2} = S^{1} \times S^{1}$. Actually two particular systems are…
We show that the KdV and the NLS equations are tri-Hamiltonian systems. We obtain the third Hamiltonian structure for these systems and prove Jacobi identity through the method of prolongation. The compatibility of the Hamiltonian…
A multiparameter class of integrable systems is introduced.
We analyse the geometry of four-dimensional bosonic manifolds arising within the context of $N=4, D=1$ supersymmetry. We demonstrate that both cases of general hyper-K\"ahler manifolds, i.e. those with translation or rotational isometries,…
In this paper we construct the supersymmetric tensor hierarchy of N=1, d=4 supergravity. We find some differences with the general bosonic construction of 4-dimensional gauged supergravities. The global symmetry group of N=1,d=4…
We classify all the supersymmetric configurations of ungauged N=2,d=4 supergravity coupled to n vector multiplets and determine under which conditions they are also classical solutions of the equations of motion. The supersymmetric…