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

J. Golenia·Y. A. Prykarpatsky·A. M. Samoilenko·A. K. Prykarpatsky
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Abstract

The structure properties of multidimensional Delsarte transmutation operators in parametirc functional spaces are studied by means of differential-geometric 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 commutive differential operator expressions related via a Darboux-Backlund transformation having a lot of applications in solition theory. Some results are also sketched concerning theory of Delsarte transmutation operators for affine polynomial pencils of multidimensional differential operators.

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J. Golenia, Y. A. Prykarpatsky, A. M. Samoilenko, A. K. Prykarpatsky. 2004-04-06. The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2. https://arxiv.org/abs/math-ph/0404016

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