Opuscula Mathematica

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

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



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.
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
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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