Physics – Mathematical Physics
Scientific paper
2004-03-29
Physics
Mathematical Physics
12 pages
Scientific paper
The structure properties of multidimensional Delsarte-Darboux transmutation operators in parametric functional spaces is 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.
Prykarpatsky Anatoliy K.
Prykarpatsky Yarema A.
Samoilenko Anatoliy M.
Samoylenko Valeriy H.
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