The Delsarte-Darboux type binary transformations and their differential-geometric and operator structure. Part 1
Mathematical Physics
2007-05-23 v1 Dynamical Systems
math.MP
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.
Cite
@article{arxiv.math-ph/0403055,
title = {The Delsarte-Darboux type binary transformations and their differential-geometric and operator structure. Part 1},
author = {Y. A. Prykarpatsky and A. M. Samoilenko and A. K. Prykarpatsky and V. Hr. Samoylenko},
journal= {arXiv preprint arXiv:math-ph/0403055},
year = {2007}
}
Comments
12 pages