N=1, D=10 Tensionless Superbranes I

We consider a model for tensionless (null) super p-branes in the Hamiltonian approach and in the framework of a harmonic superspace. The obtained algebra of Lorentz-covariant, irreducible, first class constraints is such that the BRST charge corresponds to a first rank system.Comment: 10 pages, LaTeX, no figure

Properties of Supersymmetric Integrable Systems of KP Type

The recently proposed supersymmetric extensions of reduced Kadomtsev-Petviashvili (KP) integrable hierarchies in $N =1,2$ superspace are shown to contain in the purely bosonic limit new types of ordinary non-supersymmetric integrable systems. The latter are coupled systems of several multi-component non-linear Schr{\"o}dinger-like hierarchies whose basic nonlinear evolution equations contain additional quintic and higher-derivative nonlinear terms. Also, we obtain the N=2 supersymmetric extension of Toda chain model as Darboux-B{\"a}cklund orbit of the simplest reduced N=2 super-KP hierarchy and find its explicit solution.Comment: EPJ LaTeX Style, 4 pages, minor typos corrected and references added Talk at "Geometry, Integrability and Nonlinearity in Condensed Matter and Soft Condensed Matter Physics", July 2001, Bansko (Bulgaria

Constrained KP Hierarchies: Additional Symmetries, Darboux-B\"{a}cklund Solutions and Relations to Multi-Matrix Models

This paper provides a systematic description of the interplay between a specific class of reductions denoted as \cKPrm ($r,m \geq 1$) of the primary continuum integrable system -- the Kadomtsev-Petviashvili ({\sf KP}) hierarchy and discrete multi-matrix models. The relevant integrable \cKPrm structure is a generalization of the familiar $r$-reduction of the full {\sf KP} hierarchy to the $SL(r)$ generalized KdV hierarchy ${\sf cKP}_{r,0}$. The important feature of \cKPrm hierarchies is the presence of a discrete symmetry structure generated by successive Darboux-B\"{a}cklund (DB) transformations. This symmetry allows for expressing the relevant tau-functions as Wronskians within a formalism which realizes the tau-functions as DB orbits of simple initial solutions. In particular, it is shown that any DB orbit of a ${\sf cKP}_{r,1}$ defines a generalized 2-dimensional Toda lattice structure. Furthermore, we consider the class of truncated {\sf KP} hierarchies ({\sl i.e.}, those defined via Wilson-Sato dressing operator with a finite truncated pseudo-differential series) and establish explicitly their close relationship with DB orbits of \cKPrm hierarchies. This construction is relevant for finding partition functions of the discrete multi-matrix models. The next important step involves the reformulation of the familiar non-isospectral additional symmetries of the full {\sf KP} hierarchy so that their action on \cKPrm hierarchies becomes consistent with the constraints of the reduction. Moreover, we show that the correct modified additional symmetries are compatible with the discrete DB symmetry on the \cKPrm DB orbits. The above technical arsenal is subsequently applied to obtain completeComment: LaTeX, 63 pg