TY  - JOUR
ID  - Golenia2004
LB  - Golenia2004
AU  - Golenia, J.
AU  - Prykarpatsky, Y. A.
AU  - Samoilenko, A. M.
AU  - Prykarpatsky, A. K.
TI  - The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2
ST  - The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2004
VL  - 24
IS  - 1
SP  - 71
EP  - 83
DO  - http://dx.doi.org/10.7494/OpMath.2004.24.1.71
UR  - http://dx.doi.org/10.7494/OpMath.2004.24.1.71
AB  - The structure properties of multidimensional Delsarte transmutation operators in parametric functional spaces are studied by means of differential-geometric 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 commutive differential operator expressions related via a Darboux-Backlund transformation having a lot of applications in soliton theory. Some results are also sketched concerning theory of Delsarte transmutation operators for affine polynomial pencils of multidimensional differential operators.
KW  - Delsarte transmutation operators
KW  - parametric functional spaces
KW  - Darboux transformations
KW  - inverse spectral transform problem
KW  - soliton equations
KW  - Zakharov-Shabat equations
KW  - polynomial operator pencils
SN  - 1232-9274
ER  -