  The structure properties of multidimensional Delsarte-Darboux transmutation
operators in parametric functional spaces is studied by means of
differential-geometric and topological tools. It is shown that kernels of the
corresponding integral operator expressions depend on the topological structure
of related homological cycles in the coordinate space. As a natural realization
of the construction presented we build pairs of Lax type commutative
differential operator expressions related via a Delsarte-Darboux transformation
and having a lot of applications in soliton theory.
