adiunkt
Wydział Matematyki Stosowanej WMS-krr, Katedra Równań Różniczkowych
ORCID: 0000-0002-3033-7419 połącz konto z ORCID
ResearcherID: U-8877-2017
Scopus: 6603328340
A survey of the spectral and differential geometric aspects of the generalized De Rham-Hodge theory related with Delsarte transmutation operators in multidimension and applications to spectral and soliton problems, Pt. 1 / Yarema A. PRYKARPATSKY, Anatoliy M. Samoilenko, Anatoliy K. PRYKARPATSKY // Applied Mathematics E-Notes [Dokument elektroniczny]. — Czasopismo elektroniczne ; ISSN 1607-2510. — 2005 vol. 5, s. 210–246. — Bibliogr. s. 244–246, Abstr.. — tekst: https://www.emis.de/journals/AMEN/2005/040619-2.pdf
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Zobacz pełny wykaz publikacji Autora/Autorów: Anatolij Prykarpatsky
cyfrowy identyfikator dokumentu:
About a scalar Lax type representation for one class of hydrodynamic systems in one dimension / PRYKARPATSKY Ya. A., Prytula M. M., Revenko V., A. // W: The eleventh international colloquium on differential equations : Plovdiv, Bulgaria, August 18–23, 2000 : abstracts of invited lectures and short communications. — [Bulgaria : s. n.], [2000]. — S. [1–2]. — Bibliogr. s. [2]
Algebro-analìtičnì aspekti cìlkom ìntegrovnih dinamìčnih sistem ta ïh zburen' — [Agebraic-analytic aspects of completely integrable dynamical systems and their perturbations] / A. M. Samojlenko, J. A. PRYKARPATSKY ; red. N. Ì. Kovalenko. — Kiïv : Ìnstitut matematiki NAN Ukraïni, 2002. — 236, [1] s.. — (Pracì Ìnstitutu matematiki Naciìonal'noï akademiï nauk Ukraïni. Matematika ta ïï zastosuvannâ ; t. 41). — Bibliogr. s. 223–236
Comparison of heterogeneous and homogenized numerical models of cavitation / Roman Samulyak, Jarema PRYKARPATSKY, Tianshi Lu, James Glimm, Zhiliang Xu, Myoung-Nyoun Kim // International Journal for Multiscale Computational Engineering ; ISSN 1543-1649. — 2006 vol. 4 iss. 3, s. 377–390. — Bibliogr., Abstr.
cyfrowy identyfikator dokumentu: 10.1615/IntJMultCompEng.v4.i3.70
Geometrične uzagal'nennja metodu Puankare dlja doslidžennja Lagranževich mnogovidiv povil'no zburenich Gamil'tonovich sistem v okoli giperboličnich osoblivich točok — [Geometrical generalization of the Poincaré methods for the investigation Lagrangian manifolds of slowly perturbed Hamiltonian systems in a neighborhood of a hyperbolic singular point] / Ja. A. PRIKARPATS'SKIJ, A. M. Samojlenko // Nelìnìjnì Kolivannâ ; ISSN 1562-3076. — 2000 t. 3 no. 2, s. 246–255. — Bibliogr. s. 255
Integrability by quadratures of Hamiltonian systems and Picard-Fuchs type equations: the modern differential-geometric aspects / Y. A. PRYKARPATSKY, A. M. Samoilenko, D. L. Blackmore, A. K. PRYKARPATSKY // Miskolc Mathematical Notes ; ISSN 1787-2405. — 2005 vol. 6 no. 1, s. 65–103. — Bibliogr. s. 101–102, Abstr.
Kanonìčna redukcìâ na kodotičnih simplektičnih mnogovidah ìz grupovoû dìêû ta na asocìjovanih golovnih rozšaruvannâh ìz zv'âznìstû — [Canonical reduction on cotangent symplectic manifolds with a group action and on associated principal fiber bundles with connection] / J. A. PRYKARPATSKY // Nelìnìjnì Kolivannâ = Nonlinear Oscillations ; ISSN 1562-3076. — 2006 t. 9 no. 1, s. 98–108. — Bibliogr. s. 108
Mel'nikov-Samoilenko adiabatic stability problem / J. A. PRYKARPATSKY // Ukrainian Mathematical Journal ; ISSN 0041-5995. — 2006 vol. 58 no. 6, s. 887–903. — Bibliogr. s. 902–903. — J. A. Prykarpatski - pierwsza afiliacja: Ukrainian Academy of Sciences, Kyiv, Ukraine. — tekst: https://goo.gl/i7oimT
cyfrowy identyfikator dokumentu: 10.1007/s11253-006-0111-8
On a Dirac type quantization algorithm for the Neumann-Bogoliubov oscillatory dynamical system / Ya. A. PRYKARPATS'KY, M. PYTEL-KUDELA, V. Hr. Samoylenko // Nelìnìjnì Kolivannâ = Nonlinear Oscillations ; ISSN 1562-3076. — 2001 vol. 4 no. 1, s. 106–111. — Bibliogr. s. 110–111
Zobacz pełny wykaz publikacji Autora/Autorów: Marzenna Pytel-Kudela
On the Liouville-Arnold integrable flows related with quantum algebras and their Poissonian representations / Anatoliy Samoilenko, Yarema PRYKARPATSKY, Denis Blackmore, Anatolij PRYKARPATSKY // W: The proceedings of Fifth international conference “Symmetry in nonlinear mathematical physics”, Pt. 3 / eds. A. G. Nikitin [et al.]. — Kyiv : IM, 2004. — (Proceedings of Institute of Mathematics of NAS of Ukraine ; vol. 50). — S. 1184–1191. — Bibliogr. s. 1191
Pro ìntegrovnìst' odnìêï gìdrodinamìčnoï sistemi ta ïï skìnčennovimìrnih redukcìj — On integrability of some hydrodynamic system and its finite dimensional reductions / Ârema PRYKARPATSKY, Miroslava Kopič // Vìsnik L'vìvs'kogo Unìversitetu. Serìâ mehanìko-matematična ; ISSN 2078-3744. — 2003 vip. 62, s. 103–108. — Bibliogr. s. 108
Simplektičnij metod pobudovi ergodičnih mìr na ìnvarìantnih pìdmnogovidah neavtonomnih gamìl'tonovih sistem: Lagranževì mnogovidi, ïh struktura ta gomologìï Mazera — [Symplectic method of ergodic measures constructions on invariant manifolds of nonautonomous Hamiltonian systems: Lagrangian manifolds, their structure and J. Mather's homology] / J. A. PRYKARPATSKY // Ukraïns'kij Matematičnij Žurnal ; ISSN 1027-3190. — 2006 t. 58 no. 5, s. 675–691. — Bibliogr. s. 690–691
Skinčennovimirni redukcii uzagal'nenoi dinamičnoi sistemi Bjurgersa ta ich integrovnist' — [Finite-dimensional reduction of a generalized Burgers dynamical systems and its integrability] / Ja A. PRIKARPATS'KIJ, M. M. Pritula, O. E. Gentoš // Nelìnìjnì Kolivannâ ; ISSN 1562-3076. — 2000 t. 3 no. 1, s. 95–101
Struktura bìnarnih peretvoren' tipu Darbu ta ïh zastosuvannâ v teorìï solìtonìv — [The structure of Darboux type binary transformations and their applications in soliton theory] / Â. A. PRYKARPATSKY, A. M. Samojlenko, V. G. Samojlenko // Ukraïns'kij Matematičnij Žurnal ; ISSN 1027-3190. — 2003 t. 55 no. 12, s. 1704–1719. — Bibliogr. s. 1719
Symplectic method for the construction of ergodic measures on invariant submanifolds of nonautomous Hamiltonian systems : Lagrangian manifolds, their structure, and mather homologies / J. A. PRYKARPATSKY // Ukrainian Mathematical Journal ; ISSN 0041-5995. — 2006 vol. 58 no. 5, s. 763–778. — Bibliogr. s. 778. — tekst: https://goo.gl/W89M5r
The complete integrability and Picard-Fuchs equations of a four-dimensional truncated Focker-Plank Hamiltonian system, 1 / A. M. Samoilenko, Ya. A. PRYKARPATS'KY // Nelìnìjnì Kolivannâ = Nonlinear Oscillations ; ISSN 1562-3076. — 2001 vol. 4 no. 2, s. 264–271. — Bibliogr. s. 271
The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications, Pt. 2 — Bìnarnì peretvorenniâ tipu Del'sarta-Darbu, ïhnâ diferencìal'no-geometrična ta operatorna strukturi z zastosuvannâmi, [Č.] 2 / Ya. A. PRYKARPATSKY, A. M. Samoilenko // Prikladnì Problemi Mehanìki ì Matematiki ; ISSN 1810-3022. — 2004 iss. 2, s. 7–30. — Bibliogr. s. 28–30
The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications, Pt. 1 / Jarema A. PRYKARPATSKY, Anatoliy M. Samoilenko // Opuscula Mathematica ; ISSN 1232-9274. — Tytuł poprz.: Scientific Bulletins of Stanisław Staszic Academy of Mining and Metallurgy. Opuscula Mathematica. — 2006 vol. 26 no. 1, s. 137–150. — Bibliogr. s. 148–149, Abstr.. — tekst: http://journals-1bg-1agh-1edu-1pl-1ftlf1rjl0ebc.wbg2.bg.agh.edu.pl/OPUSCULA/26-1/26-1-10.pdf
keywords: Delsarte transmutation operators, parametric functional spaces, Darboux transformations, inverse spectral transform problem, soliton equations, Zakharov-Shabat equations
The ergodic measures related with nonautonomous Hamiltonian systems and their homology structure, Pt. 1 / Denis L. Blackmore, Yarema A. PRYKARPATSKY, Anatoliy M. Samoilenko, Anatoliy K. PRYKARPATSKY // Cubo : a mathematical journal / Universidad de La Frontera. Departamento de Matemáticas y Estadística ; ISSN 0716-7776. — 2005 vol. 7 no. 3, s. 49–63
The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory, Pt. 2 / J. GOLENIA, Y. A. PRYKARPATSKY, A. M. Samoilenko, A. K. PRYKARPATSKY // Opuscula Mathematica ; ISSN 1232-9274. — Tytuł poprz.: Scientific Bulletins of Stanisław Staszic Academy of Mining and Metallurgy. Opuscula Mathematica. — 2004 R. 24 [no.] 1, s. 71–83. — Bibliogr. s. 82–83, Abstr.. — tekst: https://www.opuscula.agh.edu.pl/om-vol24iss1art6
keywords: Delsarte transmutation operators, parametric functional spaces, Darboux transformations, inverse spectral transform problem, soliton equations, Zakharov-Shabat equations, polynomial operator pencils
Zobacz pełny wykaz publikacji Autora/Autorów: Anatolij Prykarpatsky, Jolanta Golenia
The generalized de Rham-Hodge theory aspects of Delsarte-Darboux type transformations in multidimension / Anatoliy Mykhaylovich Samoilenko, Yarema Anatoliyovych PRYKARPATSKY, Anatoliy Karolevych PRYKARPATSKY // Central European Journal of Mathematics ; ISSN 1895-1074. — 2005 vol. 3 no. 3, s. 529–557. — Bibliogr. s. 554–557, Abstr.. — tekst: https://link-1springer-1com-1nyztlj1y06b6.wbg2.bg.agh.edu.pl/content/pdf/10.2478%2FBF02475922.pdf
keywords: Delsarte transmutation operators, generalized de Rham-Hodge differential complex, parametric functional spaces, Darboux transformations, inverse spectral transform problem, soliton equations, Laplace and Dirac type operators, Zakharov-Shabat equations
The geometric properties of reduced canonically symplectic spaces with symmetry, their relationship with structures on associated principal fiber bundles and some applications, Pt. 1 / Yarema A. PRYKARPATSKY, Anatoliy M. Samoilenko, Anatolij K. PRYKARPATSKY // Opuscula Mathematica ; ISSN 1232-9274. — Tytuł poprz.: Scientific Bulletins of Stanisław Staszic Academy of Mining and Metallurgy. Opuscula Mathematica. — 2005 vol. 25 no. 2, s. 287–298. — Bibliogr. s. 296–297, Abstr.. — Y. A. Prykarpatsky - pierwsza afiliacja: The Institute of Mathematics, NAS, Kyiv, Ukraine. — tekst: http://journals-1bg-1agh-1edu-1pl-1ftlf1r1y06c9.wbg2.bg.agh.edu.pl/OPUSCULA/25-2/25-2-11.pdf
keywords: symplectic structures, Hamiltonian reduction, connections, principal fiber bundles, Yang–Mills type gauge fields
The Hodge theory of multidimensional Delsarte transmutation differential operators and its application for integrable nonlinear dynamical systems / K. PRYKARPATSKY, D. Blackmore, J. A. PRYKARPATSKY // W: ECMI 2004 : the 13\textsuperscript{th} European Conference on Mathematics in Industry : June 21–25, 2004, Eindhoven, The Netherlands. — [The Netherlands : Technische Universiteit Eindhoven], [2004]. — S. 240. — Bibliogr. s. 240
The multidimensional Delsarte transmutation operators, their differential-geometric structure and applications, Pt. 1 / Anatoliy K. PRYKARPATSKY, Anatoliy M. Samoilenko, Yarema A. PRYKARPATSKY // Opuscula Mathematica ; ISSN 1232-9274. — Tytuł poprz.: Scientific Bulletins of Stanisław Staszic Academy of Mining and Metallurgy. Opuscula Mathematica. — 2003 R. 23, s. 71–80. — Bibliogr. s. 79–80, Abstr.. — tekst: https://www.opuscula.agh.edu.pl/vol23/1/23-1-07.pdf
keywords: Delsarte transmutation operators, Darboux transformations, inverse spectral transform problem
The study of Delsarte-Lions type binary transformations, their differential-geometric and operator structure with applications, Pt. 2 / Jarema A. Prykarpatsky, Anatoliy M. Samoilenko // Opuscula Mathematica ; ISSN 1232-9274. — Tytuł poprz.: Scientific Bulletins of Stanisław Staszic Academy of Mining and Metallurgy. Opuscula Mathematica. — 2007 vol. 27 no. 1, s. 113–130. — Bibliogr. s. 127–130, Abstr.. — tekst: https://goo.gl/Lfn4mP
keywords: Delsarte transmutation operators, generalized de Rham-Hodge differential complex, Delsarte-Lions type transformations, Gelfand-Levitan-Marchenko type integral equations, mulktidimensional differential operator pencils