The multidimensional Delsarte transmutation operators, their differential-geometric structure and applications. Pt. 1

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

Abstrakty

EN

A differential-geometric structure of Delsarte transmutation operators in multidimension is desribed, application to the inverse spectral transform problem is discussed.

Słowa kluczowe

EN

Delsarte transmutation operators; Darboux transformations; inverse spectral transform problem

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2003
• Tom: Vol. 23
• Strony: 71--80
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Prykarpatsky A.K.

• Department of Applied Mathematics, AGH University of Science and Technology, Cracow, Poland
• Dept. of Nonlinear Mathematical Analysis at IAPMM, NAS of Ukraine, Lviv 01601 Ukraina

autor

Samoilenko A.M.

• Institute of Mathematics at the NAS, Kiev 01601 Ukraine

autor

Prykarpatsky Y.A.

• Brookhaven Nat. Lab. CDIC, NY, 11973 USA

Bibliografia

• [1] Delsarte J.: Sur certaines transformations fonctionelles relative aux eqautions lineaires aux derives partielles du second ordre. C. R. Acad. Sci. Paris, 1938, v. 206, p. 178-182
• 2] Delsarte J., Lions J.: Transmutations d'operateurs differentielles dans le domain complexe. Comment. Math. Helv., 1957, v. 52, p. 113-128
• [3] Marchenko V. A.: Spectral theory of Sturm-Liouville operators. Kiev, Nauk. Dumka Publ. 1972 (in Russian)
• [4] Levitan B.M., Sargsian I.S.: Sturm-Liouville and Dirac operators. Moscow, Na uka Publ. 1988 (in Russian)
• [5] Matveev V. B., Salle M.I.: Darboux-Backlund transformations and applications. NY, Springer 1993
• [6] Nizhnik L. P.: Inverse scattering problems for hyperbolic equations. Kiev, Nauk. Dumka Publ., 1991 (in Russian)
• [7] Samoilenko A.M., Prykarpatsky Y. A., Samoylenko V. G.: The structure of Darboux-type binary transformations and their applications in soliton theory. Ukr. Mat. Zhurnal, 2003, v. 56, N4.
• [8] Samoilenko A.M., Prykarpatsky Y. A.: Algebraic-analytic aspects of completely integrable dynamical systems and their perturbations. Kyiv, NAS, Inst. Mathem. Publisher 2002, v. 41 (in Ukrainian)
• [9] Nimmo J.C. C: Darboux transformations from reductions of the KP-hierarchy. Preprint of the Dept. of Mathem. at the University of Glasgow, November 8, 2002, 11 p
• [10] Prykarpatsky A. K., Mykytiuk LV.: Algebraic integrability of nonlinear dynamical systems on manifolds: classical and quantum aspects. Kluwer Acad. Publishers, the Netherlands, 1998
• [11] Godbillon C: Geometrie differentielle et mechanique analytique. Paris, Hermann 1969