Discrete transformation for matrix 3-waves problem in three dimensional space

Discrete transformation for 3- waves problem is constructed in explicit form. Generalization of this system on the matrix case in three dimensional space together with corresponding discrete transformation is presented also.Comment: LaTeX, 16 page

UV manifold and integrable systems in spaces of arbitrary dimension

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 solution of them is presented in explicit form

Fermionic flows and tau function of the N=(1|1) superconformal Toda lattice hierarchy

An infinite class of fermionic flows of the N=(1|1) superconformal Toda lattice hierarchy is constructed and their algebraic structure is studied. We completely solve the semi-infinite N=(1|1) Toda lattice and chain hierarchies and derive their tau functions, which may be relevant for building supersymmetric matrix models. Their bosonic limit is also discussed.Comment: 11 pages, no figures, revised version published in Nucl. Phys.