The Delsarte-Darboux type binary transformations and their differential-geometric and operator structure. Part 1

摘要

The structure properties of multidimensional Delsarte-Darboux transmutationoperators in parametric functional spaces is studied by means ofdifferential-geometric and topological tools. It is shown that kernels of thecorresponding integral operator expressions depend on the topological structureof related homological cycles in the coordinate space. As a natural realizationof the construction presented we build pairs of Lax type commutativedifferential operator expressions related via a Delsarte-Darboux transformationand having a lot of applications in soliton theory.