%0 Journal Article
%F Prykarpatsky2006
%A Prykarpatsky, Yarema A.
%A Samoilenko, Anatoliy M.
%T The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 1
%! The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 1
%J Opuscula Mathematica
%O Opuscula Math.
%D 2006
%V 26
%N 1
%P 137-150
%U http://www.opuscula.agh.edu.pl/vol26/1/art/opuscula_math_2610.pdf
%X The structure properties of multidimensional Delsarte-Darboux transmutation operators in parametric functional spaces are 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.
%K Delsarte transmutation operators
parametric functional spaces
Darboux transformations
inverse spectral transform problem
soliton equations
Zakharov-Shabat equations
%@ 1232-9274