Anatolij K. Prykarpatski

Designation:
Professor
Department:
Department of Physics & Mathematics
University:
Cracov University of TechnologyPoland
Country:
Poland
Email:
pryk.anat@ua.fm
Journal Associated: Annals of Mathematics and Physics Biography:

Research Interest: Lagrangian and Hamiltonian mechanics; classical and quantum electrodynamics; relativity theory, string theory and gravity; classical and quantum statistical physics and kinetic theory; quantum scattering theory; quantization problems in quantum mechanics and applications; quantum nonlinear optics; quantum Josephson type media; polaron theory; magnetohydrodynamics of plasma physics; hydrodynamics and turbulence theory; vortex theory aspects in magneto-dynamics; ergodic processes and dynamical chaos; solvable models of quantum statistical physics and elds theory

1. Integrable Dynamical Systems: di¤ erential-geometric and spectral as-
pects (monograph), Kiev, Naukova Dumka, 1987

2. Algebraic aspects of Nonlinear Dynamical Systems on Manifolds (mono-
graph), Kiev, Naukova Dumka, 1991

3. Algebraic integrability of nonlinear dynamical systems on manifolds:
classical and quantum aspects.(monograph) 1998, Kluwer Publishers, Dordrecht, the
Netherlands

4. Quantum Field Theory with Application to Quantum Nonlinear Op-
tics, World Scienti…c Publishers, 2002, New Jersey, USA

5. Di¤ erential-geometric and Lie-algebraic backgrounds of nonlinear in-
tegrable dynamical systems on functional manifolds, Second Edition, Lviv Univer-
sity Publisher, 2006, Lviv, Ukraine

6. Non linear dynamical systems of mathematical physics: spectral and dif-
ferential geometrical integrability analysis. (monograph) World Scienti…c Publ., NJ,
USA, 2011

Selected Articles:
1. The Lax solution to a Hamilton-Jacobi equation and its generalizations.: part II.
Nonlinear Analysis (USA), 2003, v.55, p. 629-640.(with Y.V. Mykytyuk and D.L. Black-
more)

2. The reduction method in the theory of Lie-algebraically inte-grable oscillatory Hamil-
tonian systems. Ukrainian Mathem.Journal. 2003, 55, N2, p. 232-240 (with V. Samoylenko
and U. Taneri)

3. The structure of Hermitean Darboux-Backlund transformations and their applica-
tions. Ukr. Mathem. Journal, 2003, v. 55, N4. (with V.G. Samoylenko)

4. On some class of factorized operator dynamical systems and their integrability. Mathematical Methods
and Physics-Mechanical Fields, 2003, v. 46, N2, p. 22.25 (with D.L. Blackmore)

5. The Lyapunov-Schmidt approach to studying homoclinics splitting in weakly per-
turbed Lagrangian and Hamiltonian systems. Ukrainian Mathem. Journal, 2003, v. 55,
N.1, p.66-74, 2004 (with A. Samoilenko and V. Samoylenko)

6. The Hopf algebras and the Heisenberg-Weil algebra related with integrable.‡ows.
Ukrainian Mathem. Journal, 2004, v. 56, N1, p.88-96 ( with A.M. Samoilenko, D.L. Black-
more)

7. The description of multi-agent interaction in complex systems, Journal of Nonlin.
Math. Physics, 2004 , v. 11, 3, p. 350-360 (with V.V. Ga…ychuk)

8. Replicator dynamics and mathematical description of multi-agent interaction in com-
plex systems, Journal of Nonlin. Math. Physics, 2004, v. 11, N1, p. 113-122 (with V.V.
Ga…ychuk)

9. A geometric approach to quantum holonomic computing algorithms. Mathematics
and Computers in Simulation, Elsevier Publ., 2004, v. 35, N2, p. 734-753 (with D. Black-
more and others)

11. The general di¤erential-geometric structure of multidimensional Delsarte transmu-
tation operators in parametric functional spaces and their applications in soliton theory.
Part 2. "Opuscula Mathematica", 2004, N 24, p. 71-83

12. Symplectic …eld theory approach to studying ergodic measures related with non-
autonomoues hamiltonian systems. "Universitat Jagiellonicae Acta Mathematicae", 2004,
November, p. 56-72

13. Symplectic analysis of the dynamical system associated with a stochastic replicator
Fisher type model. Applied Mathematics and Informatics series, Proceedings of the Lviv
National University, 2003, v. 6, p. 135-143 (with V.V. Ga…ychuk and M.M. Prytula)

14. Quantum chaos and its testing, "Theory of Stochastic processes", 2004, v. 10(26),
N 3-4 p.126-128 (with V. Ga…ychuk)

15. On some class of gradient dynamic systems associated with polynomial discrete
probability distribution. "Journal of Mathematical Methods and Phys.Mech. Fields", 2004,
v. 47, N1, p. 68-72 (with O. Hentosh)

16. Quantum Mathematics: Holonomic Computing Algorithms and Their Applications.
Part 2. Automatyka, wyd-wo AGH, 2004, cz.. p. 43-66

17. Pattern formation in neural dynamical systems governed by mutually Hamiltonian
and gradient vector …eld structures. "Condensed Matter Physics", 2004, v. 7, N3, p. 551-
563 (with V. V. Ga…ychuk)

18. Quantum-Holonomic computing algorithm via Lax type ‡ows on Grassmann man-
ifolds and dual momentum mappings. "Mathematical Bulletin", Lviv Sci. Society Publ.,
2004, v.1, p. 85-103 (with D. Blackmore and others)

19. Generalized de Rham-Hodge-Skrypnik theory: di¤erential-geometric and spectral
aspects. Ukrainian Mathematical Bulletin, 2005, v.2,N4, p. 550-582 (with Y. Prykarpatsky
and A. Samoilenko)

20. Ergodic dynamical systems: the order and chaos. Mathematical Bulletin, Lviv Sci.
Soc. Publ., 2005, v. 2, p. 8-15 (with M. Bogoliubov and M. Prytula)

21. Di¤erential-geometric foundations of nonlinear integrable dynamical systems on
functional manifolds, (Monography), Lviv University Publisher, The First Edition, 2005,
402 p., Lviv, Ukraine/Krakow, AGH (with O. Hentosh and M. Prytula, 2006)

22. The gradient-holonomic integrability analysis of a Whitham type nonlinear dy-
namical model for a relaxing medium with spatial memory, Nonlinearity, 2006, v. 19, p.
2115-2122 (with M. Prytula)

23. On the ergodic and spectral properties of generalized Boole transformations, Miskolc
Mathematical Notes, 2006, v. 7, N1, p. 91-99 (with J. Feldman)

24. Some analytical properties of dissolving operators related with the Cauchy problem
for a class of non-autonomous partial di¤erential equations. Part 1. Opuscula Mathematica,
2006, v. 26, N1, p. 131-136 (with M. Pytel-Kudela)

25. The integrability gradient-holonomic analysis of a nonlinear Whitham type model
for the relaxing medium with memory, Reports of the National Academy of Sciences, Kyiv,
2006, N5, p. 13-18 (with M. Prytula)

26. The spectral and di¤erential-geometric aspects of a generalized de Rham-Hodge
theory related with Delsarte transmutation operators in multi-dimension and its applica-
tions to spectral and soliton problems, Nonlinear Analysis, 2006, v. 65, N2, p. 395 (with
A. Samoilenko and Y. Prykarpatsky)

27. On Benney type hydrodynamical systems and their Boltzmann-Vlasov equations
kinetic models, the ICTP-Preprint, 2006, Trieste, Italy,IC/2006/006, p. 1-36 (with N. Bo-
golubov and D. Blackmore)

28. An in…nite-dimensional Borsuk-Ulam type generalization of the Leray-Schauder
type …xed point theorem and some applications. Ukrainian Mathematical Journal, Vol.
60, No. 1, 2008, pp. 100-106

29. The Lie-algebraic structures and integrability of di¤erential and di¤erential-di¤erence
nonlinear dynamical systems. The ICTP- Preprint, 2007, Trieste, Italy (with D. Blackmore
and N. Bogolubov (jr.)) 1. The Lax solution to a Hamilton-Jacobi equation and its gen-
eraizations.: part II. Nonlinear Analysis (USA), 2003, v.55, p. 629-640.(with Y.V. Mykytiuk
and D.L. Blackmore)

30. The reduction method in the theory of Lie-algebraically integrable oscillatory
Hamiltonian systems. Ukrainian Mathem.Journal. 2003, 55, N2, p. 232-240 (with V. Samoylenko
and U. Taneri)

31. The structure of Hermitean Darboux-Backlund transformations and their applica-
tions. Ukr. Mathem. Journal, 2003, v. 55, N4. (with V.G. Samoylenko)
32. On some class of factorized operator dynamical systems and their integrability.
Mathematical Methods and Physics-Mechanical Fields, 2003, v. 46, N2, p. 22.25 (with
D.L. Blackmore)

33. The Lyapunov-Schmidt approach to studying homoclinics splitting in weakly per-
turbed Lagrangian and Hamiltonian systems. Ukrainian Mathem. Journal, 2003, v. 55,
N.1, p.66-74 (with A. Samoilenko and V. Samoylenko), 2004

34. The Hopf algebras and the Heisenberg-Weil algebra related with integrable.‡ows.
Ukrainian Mathem. Journal, 2004, v. 56, N1, p.88-96 ( with A.M. Samoilenko, D.L. Black-
more)

35. The description of multi-agent interaction in complex systems, Journal of Nonlin.
Math. Physics, 2004 , v. 11, 3, p. 350-360 (with V.V. Ga…ychuk)

36. Replicator dynamics and mathematical description of multi-agent interaction in
complex systems, Journal of Nonlin. Math. Physics, 2004, v. 11, N1, p. 113-122 (with V.V.
Ga…ychuk)

37. A geometric approach to quantum holonomic computing algorithms. Mathemat-
ics and Computers in Simulation, Elsevier Publ., 2004, v. 35, N2, p. 734-753 (with D.
Blackmore and others)

38*. A geometrical approach to quantum holonomic computing algorithms. "Mathe-
matics and Computers in Simulation", Elsevier, 2004, v. 35, N2, p. 734-753. (with D.L.
Blackmore, A.M. Samoilenko, U.Taneri and Y.A. Prykarpatsky)

39. The general di¤erential-geometric structure of multidimensional Delsarte transmu-
tation operators in parametric functional spaces and their applications in soliton theory.
Part 2. "Opuscula Mathematica", 2004, N 24, p. 71-83

40. Symplectic …eld theory approach to studying ergodic measures related with non-
autonomous hamiltonian systems. "Universitat Jagellonicae Acta Mathematicae", 2004,
November, p. 56-72

41. Symplectic analysis of the dynamical system associated with a stochastic replicator
Fisher type model. Applied Mathematics and Informatics series, Proceedings of the Lviv
National University, 2003, v. 6, p. 135-143 (with V.V. Ga…ychuk and M.M. Prytula)

42. Quantum chaos and its testing, "Theory of Stochastic processes", 2004, v. 10(26),
N 3-4 p.126-128 (with V. Ga…ychuk)

43. On some class of gradient dynamic systems associated with polynomial discrete
probability distribution. "Journal of Mathematical Methods and Phys.Mech. Fields", 2004,
v. 47, N1, p. 68-72 (with O. Hentosh)

44. Quantum Mathematics: Holonomic Computing Algorithms and Their Applications.
Part 2. Automatyka, wyd-wo AGH, 2004, cz.. p. 43-66

45. Pattern formation in neural dynamical systems governed by mutually Hamiltonian
and gradient vector …eld structures. "Condensed Matter Physics", 2004, v. 7, N3, p. 551-
563 (with V. V. Ga…ychuk)

46*. Quantum-Holonomic computing algorithm via Lax type ‡ows on Grassmann man-
ifolds and dual momentum mappings. "Mathematical Bulletin", Lviv Sci. Society Publ.,
2004, v.1, p. 85-103 (with D. Blackmore and others)

47. On the Liouville-Arnold Integrable ‡ows related with quantum algebras and their
Poissonian representations. Publ. of the Inst. of Mathem., Kyiv, 2003-2004, Ukraina, 2004,
v.50, part 3, p. 1184-1191, 2005

48. The structure of Gelfand-Levitan -Marchenko type equations for Delsarte trans-
mutation operators of linear multidimensional di¤erential operators and operator pencils.
Part 1. Journal of Nonlin. Mathem. Physics, 2005, v.12(1), p. 73-87 (with J. Golenia and
Y. Prykarpatsky)

49. The structure of Gelfand-Levitan -Marchenko type equations for Delsrate trans-
mutation operators of linear multidimensional di¤erential opertaors and operator pencils.
Part 2. Journal of Nonlin. Mathem. Physics, 2005, v.12(3), p.381-408 (with J. Golenia, Y.
Prykarpatsky)

50*. The generalized de Rham-Hodge theory aspects of Delsarte-Darboux type trans-
formations in multidimension. Central European Journal of Mathem., 2005, 3(3), p. 1-29
(with A.Samoilenko, Y. Prykarpatsky)

51*. The De Rham-Hodge-Skrypnik theory of Delsarte transmutation operators in
multidimension and its applications. Reports on Mathem.Physics, 2005, v. 55(3), p. 351-
370 (with A. Samoilenko and Y. Prykarpatsky)

52. Integrability by quadratures of Hamiltonian systems and Picard-Fuchs type equa-
tions: the modern di¤erential-geometric aspects. Miskolc Mathem. Notes, 2005, v. 6(1), p.
65-103 (with A. Samoilenko, Y. Prykarpatsky and D. Blackmore)

53. A generalized de Rham-Hodge theory of multidimensional Delsarte transmutations
of di¤erential operators and its applications for nonlinear dynamical systems. Physics
of Particles and Nuclei, 2005, v. 36 (Suppl.), p. 110-121 (with N. Bogoliubov (jr), A.
Samoilenko and A. Prykarpatsky)

54. The geometric properties of reduced canonically symplectic spaces with symmetry,
their relationship with structures on associated principal …ber bundles and some applica-
tions. Part 1. Opuscula Mathematica, 2005, v. 25, N2, p.287-298 (with A. Samoilenko and
A. Prykarpatsky)

55. Integrability by quadratures of Hamiltonian systems and Picard-Fuchs type equa-
tions: the modern di¤erential-geometric aspects. Miskolc Mathem. Notes, 2005, v. 6(1), p.
65-103 (with A. Samoilenko, Y. Prykarpatsky and D. Blackmore)

56. Generalized de Rham-Hodge-Skrypnik theor: di¤erential-geometric and spectral
aspects. Ukrainian Mathematical Bulletin, 2005, v.2,N4, p. 550-582 (with Y. Prykarpatsky
and A. Samoilenko)

57. Ergodic dynamical systems: the order and chaos. NTSh- Mathematical Bulletin,
2005, v. 2, p. 8-15 (with M. Bogoliubov and M. Prytula)

58. A survey of the spectral and and di¤erential-geometric aspects of the generalized
de Rham-Hodge theory related with Delsarte transmutation operators in multi-dimension
and applications to spectral and soliton problems. Part 1, Applied Mathematics E-Notes,
2005, v. 5, p. 117-152

59. The ergodic measures related with non-autonomous Hamiltonian systems and their
homology structure, CUBO-Matehmatical Journal, 2005, v.7, N 3, p. 49-64 (with D. Black-
more and others)

60. A survey of the spectral and and di¤erential-geometric aspects of the generalized
de Rham-Hodge theory related with Delsarte transmutation operators in multi-dimension
and applications to spectral and soliton problems. Part 2, Applied Mathematics E-Notes,
2005, v. 6, p. 1-28

61. Construction of …nite-dimensional reductions on functional manifolds. Mathemati-
cal Methods and Phys.-Mech. Fileds, 2005, v. 48, N1, p. 7-14 ( with O. Bihun)

62. Mykola Bogolyubov - prefounder of contemporary mathematical physics and quan-
tum mathematics. Mathematical Bulletin of NTSh, v. 6 (2009), p. 6-13 (in Ukrainian)
(with A. Plichko)

63. Bulletin, Lviv Sci. Soc. Publ., 2005, v. 2, p. 8-15 (with M. Bogoliubov and M.
Prytula)

64. Di¤erential-geometric foundations of nonlinear integrable dynamical systems on
functional manifolds, (Monogra…a), Lviv University Publisher, The First Edition, 2005,
402 p., Lviv, Ukraine/Krakow, AGH (with O. Hentosh and M. Prytula, 2006

65. The gradient-holonomic integrability analysis of a Whitham type nonlinear dy-
namical model for a relaxing medium with spatial memory, Nonlinearity, 2006, v. 19, p.
2115-2122 (with M. Prytula)

66. On the ergodic and spectral properties of generalized Boole transformations, Miskolc
Mathematical Notes, 2006, v. 7, N1, p. 91-99 (with J. Feldman)

67. Some analytical properties of dissolving operators related with the Cauchy problem
for a class of non-autonomous partial di¤erential equations. Part 1. Opuscula Mathematica,
2006, v. 26, N1, p. 131-136 (with M. Pytel-Kudela)

68. The integrability gradient-holonomic analysis of a nonlinear Witham type model
for the relaxing medium with memory, Reports of the National Academy of Sciences, Kyiv,
2006, N5, p. 13-18 (with M. Prytula)

69*. The spectral and di¤erential-geometric aspects of a generalized de Rham-Hodge
theory related with Delsarte transmutation operators in multi-dimension and its applica-
tions to spectral and soliton problems, Nonlinear Analysis, 2006, v. 65, N2, p. 395 (with
A. Samoilenko and Y. Prykarpatsky)

70. On Benney type hydrodynamical systems and their Boltzmann-Vlasov equations
kinetic models, the Italy ICTP-Preprint (reviewed), 2006, IC/2006/006, p. 1-36 (with N.
Bogoliubov and D. Blackmore)

71. On generalized de Rham-Hodge complexes, the related characteristic Chern classes
and some applications to integrable multi dimensional di¤erential sytstems on Riemanni-
an manifolds. The ICTP-Preprint, 2006, Trieste, Italy, (Available at: publications.ictp.it)
IC/2006/107

72. The Lie-algebraic structures and integrability of di¤erential and di¤erential-di¤erence
nonlinear dynamical systems. The ICTP-Preprint, 2007, Trieste, Italy, (Available at: pub-
lications.ictp.it), IC/2007/029 (with D. Blackmore and N. Bogolubov (jr.))

73. Introductive backgrounds of modern quantum mathematics with application to
nonlinear dynamical systems. The ICTP-Preprint, 2007, Trieste, Italy, (Available at: pub-
lications.ictp.it), IC/2007/108 (with N. Bogolubov (jr.), U. Taneri and J. Golenia)

74. The di¤erential-geometric aspects of integrable dynamical systems. The ICTP-
Preprint, 2007, Trieste, Italy, (Available at: publica-tions.ictp.it), IC/2007/030 (with N.
Bogolubov (jr.), D. Blackmore, A. Samoilenko)

75. On the analytical structure of the Bogolubov generating functional method in classi-
cal statistical physics and related "collec-tive"variable method. The ICTP-Preprint, 2006,
Trieste, Italy, (Available at: publications.ictp.it), IC/2006/106 (with N. Bogolubov (jr.))

76. Analytical properties of an Ostrovsky-Whitham type dynamical system for a relax-
ing medium with spatial memory and its integrabil-ity. The ICTP-Preprint, 2007, Trieste,
Italy, (Available at: publica-tions.ictp.it), IC/2007/109 (with N. Bogolubov (jr.), J. Golenia
and I. Gucwa)

77. A symplectic generalization of the Peradzynski helicity theorem and some ap-
plications. The ICTP-Preprint, 2007, Trieste, Italy, (Available at: publications.ictp.it),
IC/2007/118, (with N. Bogolubov (jr.), J. Golenia)

78. A Borsuk-Ulam type generalization of the Leray-Schauder …xed point theorem. The
ICTP-Preprint, 2007, Trieste, Italy, (Available at: publications.ictp.it), IC/2007/028

79. A Symplectic Generalization of the Peradzynski Helicity Theorem and Some Ap-
plications. International Journal of Theoretical Physics, 47, 2008, p. 1919-1928 (with N.
Bogolubov (jr.) and J. Golenia)

80*. Introductive Backgrounds to Modern Quantum Mathematics with Application to
Nonlinear Dynamical Systems. International Journal of Theoretical Physics, March 25, 47:
2882-2897, 2008 (with N. Bogolubov (jr.), J. Golenia and U. Taneri)

81. The vacuum structure, special relativity theory and quantum mechanics: a …eld
theory no-geometry approach. The ICTP-Preprint, 2008, Trieste, Italy, (Available at: pub-
lications.ictp.it), IC/2008/051, arXiv:0807.3691v5 [gr-qc] 29 Jul 2008 (with N. Bogolubov
(jr.) and U. Taneri)

82. Di¤erential-geometric foundations of nonlinear integrable dynamical systems on
functional manifolds, (Monography), Lviv University Publisher, The Second Edition, re-
vised and supplemented. 2006, 408 p., Lviv, Ukraine/Krakow, AGH (with O. Hentosh and
M. Prytula)

83. Generalized de Rham-Hodge complexes, the related characteristic Chern classes,
and some applications to integrable multidimensional di¤erential systems on Riemannian
manifolds. Ukrainian Mathematical Journal, v. 59, Number 3 / March, 2007

84. Di¤erential-geometric and Lie-algebraic foundations of nonlinear dynamical systems
on functional manifolds. The Second edition, Lviv University Publisher, Lviv, Ukraine (in
Ukrainian)

85. On the complete integrability and linearization of the Nonlinear Burgers-Korteweg-
de Vries type equation (BKdV). Mathematical Methods and Physics-Mechanical Fields.
2008, v. 51, N4, p. 57-61 (with M. Prytula and M. Vovk)

86. Optimal strategy analysis of a competitive bank portfolio model of the share market.
Kyiv University of Technology and Design Proceedings. N2, 2008, p. 78-88 (with B.Yu.
Kyshakevych and I.P. Tverdokhlib)

87. A portfolio model of the share market. Abstracts of the Scienti…c Conference "Mod-
ern Problems of the Economical Cybernetucs Development", 9-10 April 2008, Kyiv, p.
30-32 (with B.Yu. Kyshakevych and I.P. Tverdokhlib)

88. Investigation of the optimal strategy analysis of a competitive bank portfolio model
of the share market. Proceedings of the Kyiv National University "Kyiv Polytechnical
Institute", N 2, 2008. (with B.Yu. Kyshakevych and I.P. Tverdokhlib)

89. Analysis of solutions of a non-canonical Hamilton-Jacobi equation using the gen-
eralized characteristics method and the Hopf-Lax representations. Nonlinear Analysis 71
(2009), p. 5084-5089 (with Miroslaw Lustyk, Julian Janus, Marzenna Pytel-Kudela)

90. On complete integrability and linearization of a nonlinear Burgers-Korteweg-de
vries type equation. Mathemetatical Methods and Physico-Mechanical Fields. 2008, 51,
N4, p. 99-102 (with M. Prytula and M. Vovk)

91. Quantum mathematics: backgrounds and some applications to nonlinear dynamical
systems. Nonlinear Oscillations, Springer, 11, N1, p. 7-20 (with N. Bogolubov (jr.), J.
Goilenia and U. Taneri)

92. The Characteristic Chern-Type Classes and Integrability of Multi-dimensional Dif-
ferential Systems on Riemannian Manifolds. 2008, p. 743-759. In World Scienti…c book:
http://www.worldscibooks.com/mathematics/7124.html, Proceedings of the ISAAC-2007
Congress: "Further Progress in Analysis", Proceedings of the 6th International ISAAC
Congress, (Ankara, Turkey 13 - 18 August 2007) (with N. Bogolubov (jr.))

93. Introductory Background to Modern Quantum Mathematics with Application to
Nonlinear Dynamical Systems, 2008, p. 760-780. In World Scienti…c book: http://www.
worldscibooks.com /mathematics/7124.html, Proceedings of the ISAAC-2007 Congress:
"Further Progress in Analysis", Proceedings of the 6th International ISAAC Congress,
(Ankara, Turkey 13 - 18 August 2007) (with J. Golenia, N. N. Bogolubov and U. Taneri)

94. The vacuum structure of vacuum, Maxwell equations and relativistic theory aspects.
The ICTP-Preprint, 2008, Trieste, Italy, (Available at: publications.ictp.it), IC/2008/091,
(with N. Bogolubov (jr))

95. The vacuum structure, special relativity theory and quantum mechanics: a return
to the …eld theory approach without geometry. Theoretical and Mathematical Physics,
160(2), 2009, p. 1079-1095 (with N. Bogolubov (jr.) and U. Taneri)

96*. The electromagnetic Lorentz condition problem and symplectic properties of
Maxwell- and Yang-Mills-type dynamical systems. J. Phys. A: Math. Theor. 42, 2009,
p. 165401 (with N. Bogolubov (jr.) and U. Taneri)

97. The Lagrangian and Hamiltonian formalism for the classical relativistic electrody-
namics models revisited. Ukr. J. Phys. 2009. Vol. 54, No. 8-9 (with N. Bogolubov (jr.))

98. The electromagnetic Dirac-Fock-Podolsky problem and symplectic properties of the
Maxwell and Yang-Mills type dynamical systems. The ICTP-Preprint, 2009, Trieste, Italy,
(Available at: publications.ictp.it), IC/2009/005, (with N. Bogolubov (jr), U. Taneri and
Y. Prykarpatsky)

99. On the complete integrability and linearization of a Burgers-Korteweg-de Vries
equation. Journal of Mathematical Sciences, Vol. 161, No. 1, 2009, p. 99-102 (with M. M.
Prytula and M. I. Vovk)

100. The algebraic structure of a linear Focker-Planck type kinetic dynamical system.
Mathematical Bulletin of NTSh, v. 6 (2009), p. 287-293 (with U. Taneri and M. Vovk)





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