The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Pt. 2

• Autorzy: Golenia J. , Prykarpatsky Y.A. , Samoilenko A.M. , Prykarpatsky A.K.
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

Delsarte transmutation operators; parametric functional spaces; Darboux transformations; inverse spectral transform problem; soliton equations; Zakharov-Shabat equations; polynomial operator pencils

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2004
• Tom: Vol. 24, no. 1
• Strony: 71--83
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Golenia J.

• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland

autor

Prykarpatsky Y.A.

• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland

autor

Samoilenko A.M.

• Institute of Mathematics at the NAS Kiev 01601, Ukraine

autor

Prykarpatsky A.K.

• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland

Bibliografia

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• [4] Levitan B. M., Sargsian I.S.: Sturm-Liouville and Dirac operators. Moscow, Nauka Publ. 1988 (Russian).
• [5] Nizhnik L. P.: Inverse scattering problems for hyperbolic equations. Kiev, Nauk. Dumka Publ. 1991 (Russian).
• [6] Prykarpatsky A. K., Samoilenko V. G., Prykarpatsky Y. A.: The multidimensional Delsarte transmutation operators, their differential-geometric structure and applications. Part 1. Opuscula Mathematicae 23 (2003).
• [7] Ablowitz M. J., Segur H.: Solitons and the inverse scattering transform. SIAM, Philadelphia, USA, 1981.
• [8] Matveev V. B., Salle M.I.: Darboux-Backlund transformations and applications. NY, Springer 1993.
• [9] Prykarpatsky Y. A., Samoilenko A.M., Samolyenko V. G.: The structure of Darboux-type binary transformations and their applications in soliton theory. Ukr. Mat. Zhurnal 55 (2003), N12, 1704-1719 (Ukrainian).
• [10] Samoilenko A.M., Prykarpatsky Y. A.: Algebraic-analytic aspects of completely integrable dynamical systems and their perturbations. Kyiv, NAS, Inst. Mathem. Publisher 41 (2002) (Ukrainian).
• [11] Nimmo J.C.C.: Darboux transformations from reductions of the KP-hierarchy. Preprint ol the Dept. ol Mathem. at the University ol Glasgow, November 8, 2002, 11.
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• [13] Berezin F. A., Shubin M. A.: The equation of Schrodinger. Moscow, Nauka Publ. 1983 (Russian).
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• [15] Prykarpatsky A. K., Samoylenko V. G.: The structure of binary Darboux-Delsrate transformations for Hermitian conjugated differential operators. Ukr. Mathem. Journal 6 (2004), N2, 270-274 (Ukrainian).