@Article{Golenia2004,
author = "Golenia, J. and Prykarpatsky, Y. A. and Samoilenko, A. M. and Prykarpatsky, A. K.",
title = "The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2",
journal = "Opuscula Math.",
year = "2004",
volume = "24",
number = "1",
pages = "71--83",
doi = "http://dx.doi.org/10.7494/OpMath.2004.24.1.71",
url = "http://dx.doi.org/10.7494/OpMath.2004.24.1.71",
abstract = "The structure properties of multidimensional Delsarte transmutation operators in parametric 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 soliton theory. Some results are also sketched concerning theory of Delsarte transmutation operators for affine polynomial pencils of multidimensional differential operators.",
keywords = "Delsarte transmutation operators, parametric functional spaces, Darboux transformations, inverse spectral transform problem, soliton equations, Zakharov-Shabat equations, polynomial operator pencils",
issn = "1232-9274"
}