  A version of the binary Darboux transformation is constructed for
non-stationary Schroedinger equation in dimension $k+1$, where $k$ is the
number of space variables, $k \geq 1$. This is an iterated GBDT version. New
families of non-singular and rational potentials and solutions are obtained.
Some results are new for the case that $k=1$ too. A certain generalization of a
colligation introduced by M.S. Livsic and of the $S$-node introduced by L.A.
Sakhnovich is successfully used in our construction.
