@Article{Prykarpatsky2006,
author = "Prykarpatsky, Yarema A. and Samoilenko, Anatoliy M.",
title = "The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 1",
journal = "Opuscula Math.",
year = "2006",
volume = "26",
number = "1",
pages = "137--150",
doi = "http://dx.doi.org/10.7494/OpMath.2006.26.1.137",
url = "http://dx.doi.org/10.7494/OpMath.2006.26.1.137",
abstract = "The structure properties of multidimensional Delsarte-Darboux transmutation operators in parametric functional spaces are 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.",
keywords = "Delsarte transmutation operators, parametric functional spaces, Darboux transformations, inverse spectral transform problem, soliton equations, Zakharov-Shabat equations",
issn = "1232-9274"
}