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Research

• Dynamical systems theory
• Functional and Nonlinear analysis
• Differential geometry and applications
• Integrability in mathematical physics
• Classical and quantum field theory
• Electromagnetism and electrodynamics
• Classical and quantum statistical physics

Publications

Monographs:

1. Integrable Dynamical Systems: di¤ erential-geometric and spectral aspects (monograph), Kiev, Naukova Dumka, 1987  (jointly with: Yu. Mitropolsky, N. Bogolubov, V. Samoilenko)
2. Algebraic aspects of Nonlinear Dynamical Systems on Manifolds (monograph), Kiev, Naukova Dumka, 1991 (jointly with: I. Mykytyuk)
3. Algebraic integrability of nonlinear dynamical systems on manifolds: classical and quantum aspects.(monograph) 1998, Kluwer Publishers, Dordrecht, the Netherlands (jointly with: I. Mykytyuk)
4. Quantum Field Theory with Application to Quantum Nonlinear Optics, World Scientific Publishers, 2002, New Jersey, USA  (jointly with: N. Bogolubov, U. Taneri)
5. Differential-geometric and Lie-algebraic backgrounds of nonlinear integrable dynamical systems on functional manifolds, Second Edition, Lviv University Publisher, 2006, Lviv, Ukraine  (jointly with: O. Hentosh, M. Prytula)
6. Non linear dynamical systems of mathematical physics: spectral and differential geometrical integrability analysis. (monograph) World Scientific Publ., NJ, USA, 2011 (jointly with: D. Blackmore, V. Samoylenko)

Selected articles:

1. "Generalized Lie-algebraic structures related to integrable dispersionless dynamical systems and their application"Journal of Mathematical Sciences and Modelling, 1 (1) (2018) 1-9: www.dergipark.gov.tr/jmsm,  (by Oksana E. Hentosh and others)
2. "Pfeiffer-Sato solutions of Buhl’s problem and a Lagrange-D’Alembert principle for Heavenly equations" In: a book: "Nonlinear Systems and Their Remarkable Mathematical Structures"  Norbert Euler (editor), July 3, 2018: (by Oksana E Hentosh and others)
3. "New fractional nonlinear integrable Hamiltonian systems". Applied Mathematics Letters 88 (2019) 41-49; www.elsevier.com/locate/aml (by Oksana Ye. Hentosh and others)
4. "On the solutions to the Witten-Dijkgraaf-Verlinde-Verlinde associativity equations and their algebraic properties", Journal of Geometry and Physics 134 (2018) 77-83; journal homepage: www.elsevier.com/locate/geomphys, (by Anatolij K. Prykarpatski)
5. "A novel integrability analysis of a generalized Riemann type hydrodynamic hierarchy", Miskolc Mathematical Notes Vol. 19 (2018), No. 1, pp. 555-567 DOI: 10.18514/MMN.2018.2338 (by A.M. Samoilenko, Y.A. Prykarpatsky, D. Blackmore and A.K. Prykarpatski)
6. A discrete nonlinear Schredinger type hierarchy, its finite-dimensional reduction analysis and numerical integration scheme, Journal of Mathematical Sciences, Vol. 231, No. 6, June, 2018 (with J. Cieslinski)
7. New integrable di¤erential-di¤erence and fractional nonlinear dynamical systems and their algebro-analytical properties, Commun Nonlinear Sci Numer Simulat 64 (2018) 256-268, (by: Anatolij Prykarpatski)
8. On the solutions to the Witten-Dijkgraaf-Verlinde-Verlinde associativity equations and their algebraic properties, Journal of Geometry and Physics 134 (2018) 77-83 (by: Anatolij K. Prykarpatski)
9. "Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators", Topol. Algebra Appl. 2018; 6:43-52; (by: Orest D. Artemovych, Anatolij K. Prykarpatski, and Denis L. Blackmore)
10. Linearization Covering Technique and its Application to Integrable Nonlinear Differential Systems, Symmetry, Integrability and Geometry: Methods and Applications, SIG-MA 14 (2018), 02, 15 pages, "On the (by: Anatolij K. Prykarpatski)
11. "Generalized multidimensional Boole type transformations, their discretization and ergodicity, Chaotic Modeling and Simulation, CMSIM 3: 369-376, 2018; (by: Anatolij K. Prykarpatski)
12. Theory of Multidimensional Delsarte-Lions Transmutation Operators. I, Ukrainian Mathematical Journal, 2019, Volume 70, Issue 12, pp 1913-1952
13. Theory of Multidimensional Delsarte-Lions Transmutation Operators. II, Ukrainian Mathematical Journal, 2019, Volume 71, Issue 2, pp 345-361 (with A.M. Samoilenko and others)
14. Ergodic deformations of nonlinear Hamilton systems and local homeomorphism of metric spaces, Journal of Mathematical Sciences, 2019, Vol. 241, No.1, p. 27-35 (with T. Banakh)
15. Quantum Current Algebra Symmetries and Integrable Many-Particle Schredinger Type Quantum Hamiltonian Operators, Symmetry, 2019, 11, 975; doi:10.3390/sym11080975 (with Dominik Prorok)
16. New fractional nonlinear integrable Hamiltonian systems, Applied Mathematics Letters 88 (2019) 41-49, (with Oksana Ye. Hentosh and others)