The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2

摘要

The structure properties of multidimensional Delsarte transmutation operatorsin parametirc functional spaces are studied by means of differential-geometrictools. It is shown that kernels of the corresponding integral operatorexpressions depend on the topological structure of related homological cyclesin the coordinate space. As a natural realization of the construction presentedwe build pairs of Lax type commutive differential operator expressions relatedvia a Darboux-Backlund transformation having a lot of applications in solitiontheory. Some results are also sketched concerning theory of Delsartetransmutation operators for affine polynomial pencils of multidimensionaldifferential operators.