  The differential-geometric and topological structure of Delsarte
transmutation operators and associated with them Gelfand-Levitan-Marchenko type
eqautions are studied making use of the De Rham-Hodge-Skrypnik differential
complex. The relationships with spectral theory and special Berezansky type
congruence properties of Delsarte transmuted operators are stated. Some
applications to multidimensional differential operators are done including
three-dimensional Laplace operator, two-dimensional classical Dirac operator
and its multidimensional affine extension, related with self-dual Yang-Mills
eqautions. The soliton like solutions to the related set of nonlinear dynamical
systemare discussed.
