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

Y. A. Prykarpatsky·A. M. Samoilenko·A. K. Prykarpatsky·V. Hr. Samoylenko
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Abstract

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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Y. A. Prykarpatsky, A. M. Samoilenko, A. K. Prykarpatsky, V. Hr. Samoylenko. 2004-03-29. The Delsarte-Darboux type binary transformations and their differential-geometric and operator structure. Part 1. https://arxiv.org/abs/math-ph/0403055

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