TY  - JOUR
ID  - Prykarpatsky2006
LB  - Prykarpatsky2006
AU  - Prykarpatsky, Yarema A.
AU  - Samoilenko, Anatoliy M.
TI  - The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 1
ST  - The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 1
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2006
VL  - 26
IS  - 1
SP  - 137
EP  - 150
DO  - http://dx.doi.org/10.7494/OpMath.2006.26.1.137
UR  - http://dx.doi.org/10.7494/OpMath.2006.26.1.137
AB  - 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.
KW  - Delsarte transmutation operators
KW  - parametric functional spaces
KW  - Darboux transformations
KW  - inverse spectral transform problem
KW  - soliton equations
KW  - Zakharov-Shabat equations
SN  - 1232-9274
ER  -