Opuscula Math. 26, no. 1 (2006), 137-150

 
Opuscula Mathematica

The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 1

Yarema A. Prykarpatsky
Anatoliy M. Samoilenko

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.

Mathematics Subject Classification: 34A30, 34B05, 34B15.

Full text (pdf)

Opuscula Mathematica - cover

Cite this article as:
Yarema A. Prykarpatsky, Anatoliy M. Samoilenko, The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 1, Opuscula Math. 26, no. 1 (2006), 137-150

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.