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

Identyfikatory
Warianty tytułu
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.
Rocznik
Tom
Strony
71--80
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
  • 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
  • Institute of Mathematics at the NAS, Kiev 01601 Ukraine
  • 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
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH4-0005-0088
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