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1
Content available The study of Delsarte-Lions type binary transformations, their differential-geometric and operator structure with applications. Pt. 2
Prykarpatsky Y. A., Samoilenko A. M.
Opuscula Mathematica
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2007
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Vol. 27, no. 1
113-130
EN
The Gelfand-Levitan integral equations for Delsarte-Lions type transformations in multidimension are studied. The corresponding spectral and analytical properties of Delsarte-Lions transformed operators are analyzed by means of the differential-geometric and topological tools. An approach for constructing Delsarte-Lions type transmutation operators for multidimensional differential expressions is devised.
2
Content available The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part. 1
Prykarpatsky Y.A., Samoilenko A.M.
Opuscula Mathematica
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2006
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Vol. 26, no. 1
137-150
EN
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.
3
Content available The geometric properties of reduced canonically symplectic spaces with symmetry, their relationship with structures on associated principal, fiber bundles and some applications. Pt. 1
Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K.
Opuscula Mathematica
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2005
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Vol. 25, no. 2
287-298
EN
The canonical reduction method on canonically symplectic manifolds is analized in detail, the relationships with the geometric properties of associated principal fiber bundles endowed with connection structures are stated. Some results devoted to studying geometrical properties of nonabelian Yang-Mills type gauge field equations are presented.
4
Content available remote The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Pt. 2
Golenia J., Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K.
Opuscula Mathematica
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2004
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Vol. 24, no. 1
71-83
EN
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.
5
Content available remote The multidimensional Delsarte transmutation operators, their differential-geometric structure and applications. Pt. 1
Prykarpatsky A.K., Samoilenko A.M., Prykarpatsky Y.A.
Opuscula Mathematica
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2003
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Vol. 23
71-80
EN
A differential-geometric structure of Delsarte transmutation operators in multidimension is desribed, application to the inverse spectral transform problem is discussed.
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