ar X iv : m at h - ph / 0 40 30 55 v 1 2 9 M ar 2 00 4 THE DELSARTE - DARBOUX TYPE BINARY TRANSFORMATIONS AND THEIR DIFFERENTIAL - GEOMETRIC AND OPERATOR STRUCTURE
نویسندگان
چکیده
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.
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