The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2
Mathematical Physics
2007-05-23 v1 math.MP
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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Cite
@article{arxiv.math-ph/0404016,
title = {The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2},
author = {J. Golenia and Y. A. Prykarpatsky and A. M. Samoilenko and A. K. Prykarpatsky},
journal= {arXiv preprint arXiv:math-ph/0404016},
year = {2007}
}
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10 pages