Прикарпатський Ярема Анатолійович
Публікації
2020
1. Prykarpatskyy Y., On the integrable Chaplygin type hydrodynamic systems and their geometric structure. Symmetry, ISSN:2073-8994, 12(5), p.697 (2020) DOI:10.3390/sym12050697
2. Hentosh O., Prykarpatskyy Y., The Lax-Sato integrable heavenly equations on functional supermanifolds and their Lie-algebraic structure. European Journal of Mathematics, ISSN:2199-675X, V.6 pp.232-247 (2020). DOI:10.1007/s40879-019-00329-4
2019
1. Hentosh O., Prykarpatskyy Y., Balinsky A., Prykarpatski A., The dispersionless completely integrable heavenly type Hamiltonian flows and their differential-geometric structure. Annals of Mathematics and Physics, ISSN:2689-7636, 2 (1) (2019), pp.011-025. DOI:10.17352/amp.000006
2. Samoilenko A.M., Prykarpatskyy Y.A., Blackmore D., Prykarpatsky A.K., Theory of multidimensional Delsarte - Lions transmutation operators. I. Ukrainian Mathematical Journal, ISSN:0041-5995, v. 70, No. 12 (2019), pp. 1913-1952. DOI:10.1007/s11253-019-01617-8
3. Samoilenko A.M., Prykarpatskyy Y.A., Blackmore D., Prykarpatsky A.K., Theory of multidimensional Delsarte - Lions transmutation operators. II. Ukrainian Mathematical Journal, ISSN:0041-5995, v. 71, No. 6 (2019), pp. 808-839. DOI:10.1007/s11253-019-01689-6
4. Hentosh O.Ye., Prykarpatskyy Y.A., Blackmore D., Prykarpatski A.K., Dispersionless Multi-Dimensional Integrable Systems and Their Related Conformal Structure Generating Equations. SIGMA, ISSN:1815-0659, v.15, No.079 (2019). DOI:10.3842/SIGMA.2019.079
2018
1. Hentosh O., Prykarpatsky Y., Blackmore D., Prykarpatski A., The dispersionless integrable systems and related conformal structure generating equations of mathematical physics. EasyChair Preprint, 624, (2018) WebPage:WebPage
2. Hentosh O.E., Prykarpatsky Y.A., Blackmore D., Prykarpatski A., Generalized Lie-algebraic structures related to integrable dispersionless dynamical systems and their application. Journal of Mathematical Sciences and Modelling, ISSN:2636-8692, 1 (2) (2018), pp. 105-130. DOI:10.33187/jmsm.435466
3. Prytula M.M., Hentosh O.E., Prykarpatskyy Y.A., Differential-geometric structure and the Lax-Sato integrability of a class of dispersionless heavenly type equations. Ukrainian Mathematical Journal, ISSN:0041-5995, v. 70, No. 2 (2018), pp. 293-297. DOI:10.1007/s11253-018-1503-2
4. Hentosh O.E., Prykarpatsky Y.A., Blackmore D., Prykarpatski A., Pfeiffer-Sato solutions of Buhl's problem and a Lagrange-D'Alembert principle for Heavenly equations. In Nonlinear Systems and Their Remarkable Mathematical Structures: Volume I, edited by Norbert Euler, ISBN:9781138601000, P.588, CRC Press (Boca Raton, FL, USA), (2018). WebPage:WebPage, Contents, Preface and list of Authors
5. Prykarpatsky Y., Samoilenko A., The classical M.A. Buhl problem, its Pfeiffer-Sato solutions and the classical Lagrange-d'Alambert principle for the integrable heavenly type nonlinear equations. Ukrainian Mathematical Journal, ISSN:0041-5995, v. 69, No. 12 (2018), pp. 1924-1967. DOI:10.1007/s11253-018-1480-5
6. Prykarpatski A., Samoilenko A., Blackmore D., Prykarpatskyy Y., A novel integrability analysis of a generalized Riemann type hydrodynamic hierarchy. Miskolc Mathematical Notes, ISSN:1787-2405, Vol. 19, No. 1, pp. 555-567 (2018). DOI:10.18514/MMN.2018.2338
7. Prykarpatskyy Y., Steen-Ermakov-Pinney Equation and Integrable Nonlinear Deformation of the One-Dimensional Dirac Equation, Journal of Mathematical Sciences, ISSN:1072-3374, v.231, No.6, PP.1-7, (2018). DOI:10.1007/s10958-018-3851-8
2017
1. Blackmore D., Prykarpatski A., Vovk M., Pukach P., Prykarpatsky Y., The Pfeiffer-Lax-Sato type vector field equations and the related integrable versal deformations. Matematychni Studii, ISSN:1027-4634, V.48, No.2, pp.124-133 (2017). DOI:10.15330/ms.48.2.124-133
2. Vovk M., Pukach P., Hentosh O., Prykarpatsky Y., The structure of rationally factorized Lax type flows and their analytical integrability. WSEAS Transactions on Mathematics, ISSN:1109-2769, v.16, pp. 322-330 (2017). WebPage:WebPage
3. Prykarpatski A., Hentosh O., Prykarpatsky Y., Geometric Structure of the Classical Lagrange-d'Alambert Principle and its Application to Integrable Nonlinear Dynamical Systems, Mathematics, ISSN:2227-7390, 5(4), 75 (2017). DOI:10.3390/math5040075
4. Hentosh O., Prykarpatsky Y., Blackmore D., Prykarpatski A., Lie-algebraic structure of Lax-Sato integrable heavenly equations and the Lagrange-d'Alembert principle. Journal of Geometry and Physics, ISSN:0393-0440, vol. 120, pp.208-227 (2017). DOI:10.1016/j.geomphys.2017.06.003
5. Prykarpatsky Y., Samoilenko A., The classical M.A. Buhl problem, its Pfeiffer-Sato solutions and the classical Lagrange-d'Alambert principle for the integrable heavenly type nonlinear equations. Ukrainian Mathematical Journal, ISSN:0041-5995, v. 69, No. 12 (2017), pp. 1652-1689. WebPage:WebPage
6. Prykarpatskyy Y., Steen-Ermakov-Pinney equation and integrable nonlinear deformation of one-dimensional Dirac equation, Nonlinear Oscillations, ISSN:1562-3076, vol. 20, No. 2 (2017) pp. 267-273. WebPage:WebPage
2016
1. Prykarpatskyy Y., The Ablowitz-Ladik hierarchy integrability analysis revisited: the vertex operator solution representation structure Journal of Nonlinear Mathematical Physics, ISSN:1402-9251, Vol. 23, No. 1 (2016) 92-107. DOI:10.1080/14029251.2016.1135644
2014
1. Blackmore D., Prykarpatsky Y.A., Bogolubov N.N. Jr., Prykarpatsky A.K., Integrability of and differential-algebraic structures for spatially 1D hydrodynamical systems of Riemann type. Chaos, Solitons & Fractals, ISSN:0960-0779, N59 (2014) PP.59-81. DOI:10.1016/j.chaos.2013.11.012
2013
1. Blackmore D., Prykarpatsky Y., Golenia J., Prykapatski A., Hidden Symmetries of Lax Integrable Nonlinear Systems. Applied Mathematics, ISSN:2152-7385, Vol. 4 No. 10C, 2013, pp. 95-116. DOI:10.4236/am.2013.410A3013
2. Blackmore D., Golenia J., Prykarpatsky A.K., Prykarpatsky Y.A. Invariant measures for discrete dynamical systems and ergodic properties of generalized Boole-type transformations. Ukrainian Mathematical Journal, ISSN:0041-5995, 2013, V65, N1, PP.47-63. DOI:10.1007/s11253-013-0764-z
3. Prykarpatsky Y., Artemovych O., Pavlov M., Prykarpatsky A., The differential-algebraic analysis of symplectic and Lax structures related with new Riemann-type hydrodynamical systems. Reports on Mathematical Physics, ISSN:0034-4877, 2013, V.71, Issue 3, PP. 305-351. DOI:10.1016/S0034-4877(13)60035-X
4. Prykarpatsky Y., Blackmore D., Golenia J., Prykarpatsky A., A vertex operator representation of solutions to the Gurevich-Zybin hydrodynamical equation Opuscula Mathematica, ISSN:1232-9274, 2013, V.33, N1, PP. 139-149. DOI:10.7494/OpMath.2013.33.1.139
5. Prykarpatsky, Y.A., A description of Lax type integrable dynamical systems via the Marsden-Weinstein reduction method. Communications in Nonlinear Science and Numerical Simulation, ISSN:1007-5704, 2013, V.18, Issue 9, PP.2295-2303. DOI:10.1016/j.cnsns.2013.01.010
6. Prykarpatsky Y., Bogolubov N.N.(jr.), The Marsden-Weinstein reduction structure of integrable dynamical systems and a generalized exactly solvable quantum superradiance model. International Journal of Modern Physics B, ISSN:0217-9792, 2013, V.27, N.08, P. 1350002. DOI:10.1142/S0217979213500021
2012
1. Blackmore D., Prykarpatsky A., Prykarpatsky Y., Isospectral integrability analysis of dynamical systems on discrete manifolds. Opuscula Mathematica, ISSN:1232-9274, 2012, V.32, N.1, PP. 41-66. DOI:10.7494/OpMath.2012.32.1.41
2. Prykarpatsky Y.A., Artemovych O.D., Pavlov M.V., Prykarpatsky A.K., Differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann hierarchy revisited. J. Math. Phys ISSN:0022-2488, 2012, N.53, 10352. DOI:10.1063/1.4761821
2011
1. Prykarpatsky Y.A., Bogolubov N.N.(jr.), Prykarpatsky A.K., Samoylenko V.H., On the complete integrability of nonlinear dynamical systems on functional manifolds within the gradient-holonomic approach. Reports on Mathematical Physics, ISSN:0034-4877, 2011, V.68, N.3, PP. 289-318. DOI:10.1016/S0034-4877(12)60011-1
2. Blackmore D., Prykarpatsky Y., Golenia J., Prykarpatsky A., The AKNS hierarchy and the Gurevich-Zybin dynamical system integrability revisited. Mathematical Bulletin of the Shevchenko Scientific Society, ISSN:1812-6774, 2011, V.8, PP. 258-282. WebPage:WebPage
3. Tverdokhlib I.P., Vovk M.I., Prykarpatsky Y.A., Fuzzy optimization of investment portfolio. Actual problems of economics, ISSN:1993-6788, 2011, V.125, PP. 329-337
2010
1. Prykarpatsky Y.A., Bogolubov N.N.(jr.), Prykarpatsky A.K., Samoylenko V.Hr., On the complete integrability of nonlinear dynamical systems on discrete manifolds within the gradient-holonomic approach. ICTP preprint, IC/2010/091, Trieste, Italy, 2010. WebPage:WebPage
2. Bogolubov N.N.(jr.), Prykarpatsky Y., Blackmorte D., Prykarpatsky A., The Lagrangian and Hamiltonian analysis of integrable infinite-dimensional dynamical systems. ICTP preprint, IC/2010/090, Trieste, Italy, 2010. WebPage:WebPage
3. Bogolubov N.N.(jr.), Prykarpatsky Y., Ghazaryan A., The Bogolubov representation of the polaron model and its completely integrable RPA-approximation. Condensed Matter Physics, ISSN:1607-324X, 2010, V.13, No. 2, PP. 23703-23713. DOI:10.5488/CMP.13.23703
2009
1. Bogolubov N. (Jr), Ghazaryan A., Prykarpatsky Y., Operator analysis of an RPA-reduced polaron model within the Bogolubov representation in magnetic field at finite temperature. Part 1. International Journal of Modern Physics B, ISSN:0217-9792, 2009, V.23, N.24, PP.4843-4853. DOI:10.1142/S0217979209053941
2. Bogolubov N.N. (Jr), Prykarpatsky A.K., Taneri U., Prykarpatsky Y.A., The electromagnetic Dirac-Fock-Podolsky problem and symplectic properties of Maxwell and Yang-Mills-type dynamical systems. ICTP preprint, IC/2009/005, Trieste, Italy, 2009. WebPage:WebPage
3. Bogolubov N.N. (Jr), Prykarpatsky A.K., Taneri U., Prykarpatsky Y.A., The electromagnetic Lorentz condition problem and symplectic properties of Maxwell- and Yang-Mills-type dynamical systems. Journal of Physics A: Math. Theor., ISSN:1751-8113, 2009, V42. DOI:10.1088/1751-8113/42/16/165401
4. Taneri U., Vovk M.I., Prykarpatsky Y.A., Prykarpatsky A.K. The electromagnetic Lorentz problem and the hamiltonian structure of the Maxwell-Yang-Mills type dynamical systems within the reduction method. Science Notes of the National University of Kyiv-Mohyla Academy, ISSN:1996-5931, 2009, V87, PP. 38-44
5. Golenia J., Prykarpatsky Y., Wachnicki E., The Cartan-Monge geometric approach to the generalized characteristic method and its application to the heat equation . Opuscula Mathematica, ISSN:1232-9274, 2009, V.29, N.1, PP.27-39. DOI:10.7494/OpMath.2009.29.1.27
2008
1. Boichuk O.A., Luchka A.Y., Pelyukh H.P., Prykarpatsky Y.A., Ronto A.M., Tkachenko V.I. Anatolii Mykhailovych Samoilenko (On his 70th birthday). Nonlinear Oscillations, ISSN:1536-0059, 2008. V11, N1. PP.4-6. DOI:10.1007/s11072-008-0009-5
2. Prykarpatskyy Y., Hamiltonian geometric connection associated with adiabatically perturbed Hamiltonian systems and adiabatic invariants existence. Ukrainian Mathematical Journal, ISSN:0041-5995, 2008, V60, N3, PP.382-387. DOI:10.1007/s11253-008-0066-z
2007
1. Prykarpatsky Y., Samoilenko A., The study of Delsarte-Lions type binary transformations, their differential-geometric and operator structure with applications. Part 2, Opuscula Matematica, ISSN:1232-9274, 2007, V.27, N1, PP.113-130. WebPage:WebPage
2. Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K., Bogolubov N.N. (Jr.), Blackmore D.L., The differential-geometric aspects of integrable dynamical systems. ICTP Preprints, IC/2007/030, 2007. WebPage:WebPage
3. Prytula M., Prykarpatsky Y., Starchak M., Computer simulation of the sin-Gordon exact solitons and soliton collisions. Mathematical Bulletin of the Shevchenko Scientific Society, ISSN:1812-6774, 2007, V4, pp.399-413. WebPage:WebPage
2006:
1. Samulyak R., Prykarpatskyy Y., Tianshi Lu, Glimm J., Zhiliang Xu, Myoung-Nyoun Kim, Comparison of Heterogeneous and Homogenized Numerical Models of Cavitation. International Journal for Multiscale Computational Engineering, ISSN:1543-1649, 2006, V.4, PP.377-389. DOI:10.1615/IntJMultCompEng.v4.i3.70
2. Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K., On the Geometrical Properties of Reduced Canonically Symplectic Spaces with Symmetry, Their Relationship with Structures on Associated Principal Fiber Bundles and Some Applictions. Dynamics of Continuous, Discrete and Impulsive Systems, ISSN:1201-3390, 2006, V.13B (suppl.), PP.159-171
3. Samoilenko A.M., Prykarpatsky Y.A., Prykarpatsky A.K. The spectral and differential-geometric aspects of a generalized de Rham-Hodge theory releated with Delsarte transmutation operators in multidimention and its applications to spectral and soliton problems. Nonlinear Analysis, ISSN:0362-546X, 2006, V.65, N2, PP.395-432. DOI:10.1016/j.na.2005.07.039
4. Prykarpatsky Y.A., Canonical reduction on cotangent symplectic manifolds with a group action and on the associated main foliations with connections. Nonlinear Oscillations, ISSN:1536-0059, 2006, V9, N1, PP.98-108. DOI:10.1007/s11072-006-0028-z
5. Prykarpatsky Y.A., The symplectic method of ergodic measures construction on invariant manifolds of nonautonomous hamiltonian systems. Lagrangian manifolds, their structure and homology of J.Mather. Ukrainian Mathematical Journal, ISSN:0041-5995, 2006, V58, N5, PP.675-691. DOI:10.1007/s11253-006-0100-y
6. Prykarpatsky Y.A., Mel'nikov-Samoilenko adiabatic stability problem. Ukrainian Mathematical Journal, ISSN:0041-5995, 2006, V58, N6, PP.787-803. DOI:10.1007/s11253-006-0111-8
7. Prykarpatsky Y.A., Samoilenko A.M., The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 1. Opuscula Mathematica, ISSN:1232-9274, 2006, V26, N1, PP.137-150. WebPage:WebPage
2005:
1. Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K. A survey of the spectral and differential generalized de Rham-Hodge theory related with Delsarte transmutation operators in multidimansion and application to spectral and soliton problems. Part 1. Applied Mathematics E-Notes, ISSN:1607-2510, 2005, N5, PP.210-246. WebPage:WebPage
2. Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K. A survey of the spectral and differential generalized de Rham-Hodge theory related with Delsarte transmutation operators in multidimansion and application to spectral and soliton problems. Part 2. Applied Mathematics E-Notes, ISSN:1607-2510, 2005, N6, PP.84-112. WebPage:WebPage
3. Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K. The generalized de Rham-Hodge-Skrypnyk theory: differential-spectral aspects and some applications. Ukrainian Mathematical Bulletin, 2005, V2, N4, PP.550-582 (in Ukrainian)
4. Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K. The de Rham-Hodge theory of Delsarte transmutation operators in multidimension and its applications. Reports on Mathematical Physics, ISSN:0034-4877, 2005, V55, N3, PP.351-370. DOI:10.1016/S0034-4877(05)80051-5
5. Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K. The geometric properties of reduced canonically symplectic spaces with symmetry, their relationship with structures on associated principal fiber bundles and some applications. Part 1. Opuscula Mathematica, ISSN:1232-9274, 2005, V25, N2, PP287-299. WebPage:WebPage
6. Samoilenko A.M., Prykarpatsky Y.A., Prykarpatsky A.K., The generalized de Rham-Hodge theory aspects of Delsarte-Darboux type transformations in multidimension. Central European Journal of Mathematics, 2005, V3, N3, pp.529-557. DOI:10.2478/BF02475922
7. Blackmore D.L., Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K. The ergodic measures related with nonautonomous hamiltonian systems and their homology structure. Part 1. CUBO A Mathematical Journal, 2005, V7, N3, PP.49-64.
8. Prykarpatsky Y.A., Samoilenko A.M., On the Lagrangian and Hamiltonian aspects of infinite-dimensional dynamical systems and their finite-dimensional reductions. Nonlinear Oscillations, ISSN:1536-0059, 2005, V8, N3, PP.360-387. DOI:10.1007/s11072-006-0007-4
9. Bogoliubov N.N., Prykarpatsky Ya.A., Samoilenko A.M., Prykarpatsky A.K., A generalized de Rham-Hodge theory of multidimensional Delsarte transmutations of differential operators and its applications for nonlinear dynamic systems. Physics of Particles and Nuclei, ISSN:1063-7796, 2005, V36, Suppl.1, PP.S110-S121.
10. Prykarpatsky Y., Samoilenko A., Blackmore D.L., Prykarpatsky A.K., Integrability by quadratures of Hamiltonian systems and Picard-Fuchs type equations: The modern differential-geometric aspects. Miskolc Mathematical Notes, ISSN:1787-2405, 2005, V6, N1, P.65-103. DOI:10.18514/MMN.2005.87
11. Golenia J., Prykarpatsky A.K., Prykarpatsky Y.A., The Structure of Gelfand-Levitan-Marchenko Type Equations for Delsarte Transmutation Operators of Linear Multidimensional Differerential Operators and Operator Pencils. Part 2. Journal of Nonlinear Mathematical Physics, ISSN:1402-9251, 2005, V12, N3, P.381-408. DOI:10.2991/jnmp.2005.12.3.5
12. Golenia J., Prykarpatsky A.K., Prykarpatsky Y.A., The Structure of Gelfand-Levitan-Marchenko Type Equations for Delsarte Transmutation Operators of Linear Multidimensional Differerential Operators and Operator Pencils. Part 1. Journal of Nonlinear Mathematical Physics, ISSN:1402-9251, 2005, V12, N1, P.73-87. DOI:10.2991/jnmp.2005.12.1.7
2004:
1. Prykarpatsky Y.A, Samoilenko A.M. The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 2. Apply Problems of Mechanics and Mathematics, Scientific Proceedings, ISSN:1810-3022, 2004, Issue 2, PP.7-30
2. Prykarpatsky Y.A., Samoilenko A.M., The generalized De Rham-Hodge-Skrypnik theory of Delsarte transmutation operators in multidimension and its applications. Nonlinear Oscillations, ISSN:1536-0059, 2004, V7, N4, P.516-537. DOI:10.1007/s11072-005-0029-3
3. Samoilenko A., Prykarpatsky Y., Blackmore D., Prykarpatsky A., On the Liouville-Arnold integrable Flows Related with quantum algebras and their Poissonian representations, Proceed. of the Inst. of Math of NAS of Ukraine, 2004, V.5, Part 3, P.1184-1191.
4. Golenia J., Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K., The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Opuscula Mathematica, ISSN:1232-9274, 2004, V24, 1, P.71-83. WebPage:WebPage
5. Samoilenko A.M., Prykarpatsky Y.A., Taneri Ufuk, Prykarpatsky A.K., Blackmore D.L., A geometrical approach to quantum holonomic computing algorithms. Mathematics and Computers in Simulations, ISSN:0378-4754, 2004, 66, P.1-20. DOI:10.1016/j.matcom.2004.01.017
6. Samulyak R., Lu T., Prykarpatskyy Y., Direct and homogeneous numerical approaches to multiphase flows and applications, Lecture Notes in Computer Science, ISSN:0302-9743, 2004. V3039. P.653-660. DOI:10.1007/978-3-540-25944-2_84
7. Samulyak R., Prykarpatskyy Y., Richtmyer-Meshkov instability in liquid metal flows: influence of cavitation and magnetic fields, Mathematics and Computers in Simulation, ISSN:0378-4754, 2004, V65, P.431-446. DOI:10.1016/j.matcom.2004.01.019
2003:
1. Prykarpatsky A.K., Samoilenko A.M., Prykarpatsky Y.A., The multidimensional Delsarte transmutation operators, their differential-geometric structure and applications. Part 1. Opuscula Mathematica, ISSN:1232-9274, 2003, V23, P. 71-79. WebPage:WebPage
2. Prykarpatsky Y., Kopych M., On integrability of a hydrodynamical system and its dimensional reductions. Visnyk Lviv Univ., Ser.Mech.-Math., 2003. V.62. P.103-108 WebPage:WebPage
3. Prykarpatsky Y.A., Samoilenko A.M., Samoilenko V.G., The structure of Darboux type binary transformations and their applications in soliton theory. Ukrainian Mathematical Journal, ISSN:0041-5995, 2003. V55, 12, P.1704-1719. DOI:10.1023/B:UKMA.0000031664.23436.5a
2002:
1. Prykarpatskyy Y. Finite dimensional local and nonlocal reductions of one type of hydrodynamic systems. Reports on Mathematical Physics, ISSN:0034-4877, 2002. V50. N3. P349-360. DOI:10.1016/S0034-4877(02)80065-9
2. Prykarpatsky Y. New approach to studing the vortex structure of Josephson media equations within the framework of Chern-Simon-Higgs Lagrangean model. Physica C, ISSN:0921-4534, 2002. V.369. P.325-330. DOI:10.1016/S0921-4534(01)01269-2
2001:
1. Prykarpatsky Ya.A., Prytula M.M., Revenko V.P. About a scalar Lax type representation for one class of hydrodynamic systems in one dimension. Reports of the National Academy of Sciences of Ukraine, ISSN:1025-6415, 2001. N8. PP.49-53
2. Samoilenko A.M.,Prykarpatsky Y.A. The complete integrabilty and Picard-Fuchs equations of a four-dimensional truncated Focker-Plank Hamiltonian system. Part 1. Nonlinear Oscillation, ISSN:1536-0059, 2001, V4, N2, P.264-271. WebPage:WebPage
3. Prykarpatsky Y., Pytel-Kudela M., Samoylenko V. On a Dirac type quantization algorithm for the Neumann-Bogoliubov oscillatory dynamical system. Nonlinear Oscillation, ISSN:1536-0059, 2001. V4. N1 P.106-111. WebPage:WebPage
2000:
1. Prykarpatsky Y.A., Samoilenko A.M. Geometrical generalization of the Poincaré methods for the investigation of Lagrangian manifolds of slowly perturbed Hamiltonian systems in a neighborhood of a hyperbolic singular point. Nonlinear Oscillations, ISSN:1536-0059, 2000, V3, N2, PP.246-255. WebPage:WebPage
2. Prykarpatsky Y.A., Prytula M.M., Hentosh O.E. Finite-dimensional reductions of a generalized Burgers dynamical systems and its integrability. Nonlinear Oscillations, ISSN:1536-0059, 2000. V3. N1. P.95-102. WebPage:WebPage
1999:
1. Prykarpatsky Y.A., Samoilenko A.M., Blackmore D.L., Embedding of integral submanifolds and associated adiabatic invariants of slowly perturbed integrable Hamiltonian systems. Reports on Mathematical Physics, ISSN:0034-4877, 1999. V44. N1-2. -P.171-182. DOI:10.1016/S0034-4877(99)80158-X
2. Samoilenko A.M., Prykarpatsky Y.A., Investigation of invariant deformations of integral manifolds of adiabatically perturbed integrable Hamiltonian systems. Part 1. Ukrainian Mathematical Journal, ISSN:0041-5995, 1999. V51. N10. -P.1379-1390. DOI:10.1007/BF02981688
3. Samoilenko A.M.,Prykarpatsky Y.A., Investigation of invariant deformations of integral manifolds of adiabatically perturbed integrable Hamiltonian systems. Part 2. Ukrainian Mathematical Journal, ISSN:0041-5995, 1999. V51. N11. -P.1513-1528. DOI:10.1007/BF02525274
4. Prykarpatsky Y.A., Samoilenko A.M., Symplectic analysis of the deformation of slowly-perturbed completely integrable Hamiltonian systems and associated adiabatic invariants. Nonlinear Oscillations, ISSN:1536-0059, 1999. V2, N1. -P.83-91. WebPage:WebPage
5. Kubes P., Prykarpatsky A.K., Zagrodzinski J., Prykarpatsky Y.A. A kinetic model of the plasma flow at the magnetic Z-pinch and the plasmoid structure. Part 2. Journal of Physical Studies, ISSN:1027-4642, 1999. V3. N1. PP.42-46. WebPage:WebPage
6. Prykarpatsky Y.A., The structure of integrable Lax flows on nonlocal manifolds: dynamical systems with sources. Journal of Mathematical Sciences, ISSN:1072-3374, 1999. V.96. N2. pp. 3030-3037. DOI:10.1007/BF02169701
1998:
1. Blackmore D.L., Prykarpatsky Y.A., Samulyak R.V. The integrability of Lie-invariant geometric objects generated by ideals in the Grasssmann algebra. Journal of Nonlinear Mathematical Physics, ISSN:1402-9251, 1998. V.5. N1. -P.54-68. DOI:10.2991/jnmp.1998.5.1.6
2. Prykarpatsky Y.A., Blackmore D.L., Hentosh O.J., Geometric structure of Lax-integrable flows on Grassmann manifolds. Collection of works of the Institute of Mathematics of NAS of Ukraine, 1998, p.41-48.
1997:
1. Kopych M., Prykarpatsky Y., Samulyak R. Adiabatic invariants of a generalized Henon-Heiles Hamiltonian system and structure of the chaotic motion. Proceeding of the National Academy of Sciences of Ukraine. 1997. N2. -P.32-36.
2. Prykarpatsky Ya.A. The structure of Lax-type integrable flows on nonlocal manifolds: dynamical systems with sources. Mathematical Methods and Physicomechanical Fields, ISSN:0130-9420, 1997. V.40. N4. -P.106-115. (in Ukrainian)
1. Prykarpatskyy Y., On the integrable Chaplygin type hydrodynamic systems and their geometric structure. Symmetry, ISSN:2073-8994, 12(5), p.697 (2020) DOI:10.3390/sym12050697
2. Hentosh O., Prykarpatskyy Y., The Lax-Sato integrable heavenly equations on functional supermanifolds and their Lie-algebraic structure. European Journal of Mathematics, ISSN:2199-675X, V.6 pp.232-247 (2020). DOI:10.1007/s40879-019-00329-4
2019
1. Hentosh O., Prykarpatskyy Y., Balinsky A., Prykarpatski A., The dispersionless completely integrable heavenly type Hamiltonian flows and their differential-geometric structure. Annals of Mathematics and Physics, ISSN:2689-7636, 2 (1) (2019), pp.011-025. DOI:10.17352/amp.000006
2. Samoilenko A.M., Prykarpatskyy Y.A., Blackmore D., Prykarpatsky A.K., Theory of multidimensional Delsarte - Lions transmutation operators. I. Ukrainian Mathematical Journal, ISSN:0041-5995, v. 70, No. 12 (2019), pp. 1913-1952. DOI:10.1007/s11253-019-01617-8
3. Samoilenko A.M., Prykarpatskyy Y.A., Blackmore D., Prykarpatsky A.K., Theory of multidimensional Delsarte - Lions transmutation operators. II. Ukrainian Mathematical Journal, ISSN:0041-5995, v. 71, No. 6 (2019), pp. 808-839. DOI:10.1007/s11253-019-01689-6
4. Hentosh O.Ye., Prykarpatskyy Y.A., Blackmore D., Prykarpatski A.K., Dispersionless Multi-Dimensional Integrable Systems and Their Related Conformal Structure Generating Equations. SIGMA, ISSN:1815-0659, v.15, No.079 (2019). DOI:10.3842/SIGMA.2019.079
2018
1. Hentosh O., Prykarpatsky Y., Blackmore D., Prykarpatski A., The dispersionless integrable systems and related conformal structure generating equations of mathematical physics. EasyChair Preprint, 624, (2018) WebPage:WebPage
2. Hentosh O.E., Prykarpatsky Y.A., Blackmore D., Prykarpatski A., Generalized Lie-algebraic structures related to integrable dispersionless dynamical systems and their application. Journal of Mathematical Sciences and Modelling, ISSN:2636-8692, 1 (2) (2018), pp. 105-130. DOI:10.33187/jmsm.435466
3. Prytula M.M., Hentosh O.E., Prykarpatskyy Y.A., Differential-geometric structure and the Lax-Sato integrability of a class of dispersionless heavenly type equations. Ukrainian Mathematical Journal, ISSN:0041-5995, v. 70, No. 2 (2018), pp. 293-297. DOI:10.1007/s11253-018-1503-2
4. Hentosh O.E., Prykarpatsky Y.A., Blackmore D., Prykarpatski A., Pfeiffer-Sato solutions of Buhl's problem and a Lagrange-D'Alembert principle for Heavenly equations. In Nonlinear Systems and Their Remarkable Mathematical Structures: Volume I, edited by Norbert Euler, ISBN:9781138601000, P.588, CRC Press (Boca Raton, FL, USA), (2018). WebPage:WebPage, Contents, Preface and list of Authors
5. Prykarpatsky Y., Samoilenko A., The classical M.A. Buhl problem, its Pfeiffer-Sato solutions and the classical Lagrange-d'Alambert principle for the integrable heavenly type nonlinear equations. Ukrainian Mathematical Journal, ISSN:0041-5995, v. 69, No. 12 (2018), pp. 1924-1967. DOI:10.1007/s11253-018-1480-5
6. Prykarpatski A., Samoilenko A., Blackmore D., Prykarpatskyy Y., A novel integrability analysis of a generalized Riemann type hydrodynamic hierarchy. Miskolc Mathematical Notes, ISSN:1787-2405, Vol. 19, No. 1, pp. 555-567 (2018). DOI:10.18514/MMN.2018.2338
7. Prykarpatskyy Y., Steen-Ermakov-Pinney Equation and Integrable Nonlinear Deformation of the One-Dimensional Dirac Equation, Journal of Mathematical Sciences, ISSN:1072-3374, v.231, No.6, PP.1-7, (2018). DOI:10.1007/s10958-018-3851-8
2017
1. Blackmore D., Prykarpatski A., Vovk M., Pukach P., Prykarpatsky Y., The Pfeiffer-Lax-Sato type vector field equations and the related integrable versal deformations. Matematychni Studii, ISSN:1027-4634, V.48, No.2, pp.124-133 (2017). DOI:10.15330/ms.48.2.124-133
2. Vovk M., Pukach P., Hentosh O., Prykarpatsky Y., The structure of rationally factorized Lax type flows and their analytical integrability. WSEAS Transactions on Mathematics, ISSN:1109-2769, v.16, pp. 322-330 (2017). WebPage:WebPage
3. Prykarpatski A., Hentosh O., Prykarpatsky Y., Geometric Structure of the Classical Lagrange-d'Alambert Principle and its Application to Integrable Nonlinear Dynamical Systems, Mathematics, ISSN:2227-7390, 5(4), 75 (2017). DOI:10.3390/math5040075
4. Hentosh O., Prykarpatsky Y., Blackmore D., Prykarpatski A., Lie-algebraic structure of Lax-Sato integrable heavenly equations and the Lagrange-d'Alembert principle. Journal of Geometry and Physics, ISSN:0393-0440, vol. 120, pp.208-227 (2017). DOI:10.1016/j.geomphys.2017.06.003
5. Prykarpatsky Y., Samoilenko A., The classical M.A. Buhl problem, its Pfeiffer-Sato solutions and the classical Lagrange-d'Alambert principle for the integrable heavenly type nonlinear equations. Ukrainian Mathematical Journal, ISSN:0041-5995, v. 69, No. 12 (2017), pp. 1652-1689. WebPage:WebPage
6. Prykarpatskyy Y., Steen-Ermakov-Pinney equation and integrable nonlinear deformation of one-dimensional Dirac equation, Nonlinear Oscillations, ISSN:1562-3076, vol. 20, No. 2 (2017) pp. 267-273. WebPage:WebPage
2016
1. Prykarpatskyy Y., The Ablowitz-Ladik hierarchy integrability analysis revisited: the vertex operator solution representation structure Journal of Nonlinear Mathematical Physics, ISSN:1402-9251, Vol. 23, No. 1 (2016) 92-107. DOI:10.1080/14029251.2016.1135644
2014
1. Blackmore D., Prykarpatsky Y.A., Bogolubov N.N. Jr., Prykarpatsky A.K., Integrability of and differential-algebraic structures for spatially 1D hydrodynamical systems of Riemann type. Chaos, Solitons & Fractals, ISSN:0960-0779, N59 (2014) PP.59-81. DOI:10.1016/j.chaos.2013.11.012
2013
1. Blackmore D., Prykarpatsky Y., Golenia J., Prykapatski A., Hidden Symmetries of Lax Integrable Nonlinear Systems. Applied Mathematics, ISSN:2152-7385, Vol. 4 No. 10C, 2013, pp. 95-116. DOI:10.4236/am.2013.410A3013
2. Blackmore D., Golenia J., Prykarpatsky A.K., Prykarpatsky Y.A. Invariant measures for discrete dynamical systems and ergodic properties of generalized Boole-type transformations. Ukrainian Mathematical Journal, ISSN:0041-5995, 2013, V65, N1, PP.47-63. DOI:10.1007/s11253-013-0764-z
3. Prykarpatsky Y., Artemovych O., Pavlov M., Prykarpatsky A., The differential-algebraic analysis of symplectic and Lax structures related with new Riemann-type hydrodynamical systems. Reports on Mathematical Physics, ISSN:0034-4877, 2013, V.71, Issue 3, PP. 305-351. DOI:10.1016/S0034-4877(13)60035-X
4. Prykarpatsky Y., Blackmore D., Golenia J., Prykarpatsky A., A vertex operator representation of solutions to the Gurevich-Zybin hydrodynamical equation Opuscula Mathematica, ISSN:1232-9274, 2013, V.33, N1, PP. 139-149. DOI:10.7494/OpMath.2013.33.1.139
5. Prykarpatsky, Y.A., A description of Lax type integrable dynamical systems via the Marsden-Weinstein reduction method. Communications in Nonlinear Science and Numerical Simulation, ISSN:1007-5704, 2013, V.18, Issue 9, PP.2295-2303. DOI:10.1016/j.cnsns.2013.01.010
6. Prykarpatsky Y., Bogolubov N.N.(jr.), The Marsden-Weinstein reduction structure of integrable dynamical systems and a generalized exactly solvable quantum superradiance model. International Journal of Modern Physics B, ISSN:0217-9792, 2013, V.27, N.08, P. 1350002. DOI:10.1142/S0217979213500021
2012
1. Blackmore D., Prykarpatsky A., Prykarpatsky Y., Isospectral integrability analysis of dynamical systems on discrete manifolds. Opuscula Mathematica, ISSN:1232-9274, 2012, V.32, N.1, PP. 41-66. DOI:10.7494/OpMath.2012.32.1.41
2. Prykarpatsky Y.A., Artemovych O.D., Pavlov M.V., Prykarpatsky A.K., Differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann hierarchy revisited. J. Math. Phys ISSN:0022-2488, 2012, N.53, 10352. DOI:10.1063/1.4761821
2011
1. Prykarpatsky Y.A., Bogolubov N.N.(jr.), Prykarpatsky A.K., Samoylenko V.H., On the complete integrability of nonlinear dynamical systems on functional manifolds within the gradient-holonomic approach. Reports on Mathematical Physics, ISSN:0034-4877, 2011, V.68, N.3, PP. 289-318. DOI:10.1016/S0034-4877(12)60011-1
2. Blackmore D., Prykarpatsky Y., Golenia J., Prykarpatsky A., The AKNS hierarchy and the Gurevich-Zybin dynamical system integrability revisited. Mathematical Bulletin of the Shevchenko Scientific Society, ISSN:1812-6774, 2011, V.8, PP. 258-282. WebPage:WebPage
3. Tverdokhlib I.P., Vovk M.I., Prykarpatsky Y.A., Fuzzy optimization of investment portfolio. Actual problems of economics, ISSN:1993-6788, 2011, V.125, PP. 329-337
2010
1. Prykarpatsky Y.A., Bogolubov N.N.(jr.), Prykarpatsky A.K., Samoylenko V.Hr., On the complete integrability of nonlinear dynamical systems on discrete manifolds within the gradient-holonomic approach. ICTP preprint, IC/2010/091, Trieste, Italy, 2010. WebPage:WebPage
2. Bogolubov N.N.(jr.), Prykarpatsky Y., Blackmorte D., Prykarpatsky A., The Lagrangian and Hamiltonian analysis of integrable infinite-dimensional dynamical systems. ICTP preprint, IC/2010/090, Trieste, Italy, 2010. WebPage:WebPage
3. Bogolubov N.N.(jr.), Prykarpatsky Y., Ghazaryan A., The Bogolubov representation of the polaron model and its completely integrable RPA-approximation. Condensed Matter Physics, ISSN:1607-324X, 2010, V.13, No. 2, PP. 23703-23713. DOI:10.5488/CMP.13.23703
2009
1. Bogolubov N. (Jr), Ghazaryan A., Prykarpatsky Y., Operator analysis of an RPA-reduced polaron model within the Bogolubov representation in magnetic field at finite temperature. Part 1. International Journal of Modern Physics B, ISSN:0217-9792, 2009, V.23, N.24, PP.4843-4853. DOI:10.1142/S0217979209053941
2. Bogolubov N.N. (Jr), Prykarpatsky A.K., Taneri U., Prykarpatsky Y.A., The electromagnetic Dirac-Fock-Podolsky problem and symplectic properties of Maxwell and Yang-Mills-type dynamical systems. ICTP preprint, IC/2009/005, Trieste, Italy, 2009. WebPage:WebPage
3. Bogolubov N.N. (Jr), Prykarpatsky A.K., Taneri U., Prykarpatsky Y.A., The electromagnetic Lorentz condition problem and symplectic properties of Maxwell- and Yang-Mills-type dynamical systems. Journal of Physics A: Math. Theor., ISSN:1751-8113, 2009, V42. DOI:10.1088/1751-8113/42/16/165401
4. Taneri U., Vovk M.I., Prykarpatsky Y.A., Prykarpatsky A.K. The electromagnetic Lorentz problem and the hamiltonian structure of the Maxwell-Yang-Mills type dynamical systems within the reduction method. Science Notes of the National University of Kyiv-Mohyla Academy, ISSN:1996-5931, 2009, V87, PP. 38-44
5. Golenia J., Prykarpatsky Y., Wachnicki E., The Cartan-Monge geometric approach to the generalized characteristic method and its application to the heat equation . Opuscula Mathematica, ISSN:1232-9274, 2009, V.29, N.1, PP.27-39. DOI:10.7494/OpMath.2009.29.1.27
2008
1. Boichuk O.A., Luchka A.Y., Pelyukh H.P., Prykarpatsky Y.A., Ronto A.M., Tkachenko V.I. Anatolii Mykhailovych Samoilenko (On his 70th birthday). Nonlinear Oscillations, ISSN:1536-0059, 2008. V11, N1. PP.4-6. DOI:10.1007/s11072-008-0009-5
2. Prykarpatskyy Y., Hamiltonian geometric connection associated with adiabatically perturbed Hamiltonian systems and adiabatic invariants existence. Ukrainian Mathematical Journal, ISSN:0041-5995, 2008, V60, N3, PP.382-387. DOI:10.1007/s11253-008-0066-z
2007
1. Prykarpatsky Y., Samoilenko A., The study of Delsarte-Lions type binary transformations, their differential-geometric and operator structure with applications. Part 2, Opuscula Matematica, ISSN:1232-9274, 2007, V.27, N1, PP.113-130. WebPage:WebPage
2. Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K., Bogolubov N.N. (Jr.), Blackmore D.L., The differential-geometric aspects of integrable dynamical systems. ICTP Preprints, IC/2007/030, 2007. WebPage:WebPage
3. Prytula M., Prykarpatsky Y., Starchak M., Computer simulation of the sin-Gordon exact solitons and soliton collisions. Mathematical Bulletin of the Shevchenko Scientific Society, ISSN:1812-6774, 2007, V4, pp.399-413. WebPage:WebPage
2006:
1. Samulyak R., Prykarpatskyy Y., Tianshi Lu, Glimm J., Zhiliang Xu, Myoung-Nyoun Kim, Comparison of Heterogeneous and Homogenized Numerical Models of Cavitation. International Journal for Multiscale Computational Engineering, ISSN:1543-1649, 2006, V.4, PP.377-389. DOI:10.1615/IntJMultCompEng.v4.i3.70
2. Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K., On the Geometrical Properties of Reduced Canonically Symplectic Spaces with Symmetry, Their Relationship with Structures on Associated Principal Fiber Bundles and Some Applictions. Dynamics of Continuous, Discrete and Impulsive Systems, ISSN:1201-3390, 2006, V.13B (suppl.), PP.159-171
3. Samoilenko A.M., Prykarpatsky Y.A., Prykarpatsky A.K. The spectral and differential-geometric aspects of a generalized de Rham-Hodge theory releated with Delsarte transmutation operators in multidimention and its applications to spectral and soliton problems. Nonlinear Analysis, ISSN:0362-546X, 2006, V.65, N2, PP.395-432. DOI:10.1016/j.na.2005.07.039
4. Prykarpatsky Y.A., Canonical reduction on cotangent symplectic manifolds with a group action and on the associated main foliations with connections. Nonlinear Oscillations, ISSN:1536-0059, 2006, V9, N1, PP.98-108. DOI:10.1007/s11072-006-0028-z
5. Prykarpatsky Y.A., The symplectic method of ergodic measures construction on invariant manifolds of nonautonomous hamiltonian systems. Lagrangian manifolds, their structure and homology of J.Mather. Ukrainian Mathematical Journal, ISSN:0041-5995, 2006, V58, N5, PP.675-691. DOI:10.1007/s11253-006-0100-y
6. Prykarpatsky Y.A., Mel'nikov-Samoilenko adiabatic stability problem. Ukrainian Mathematical Journal, ISSN:0041-5995, 2006, V58, N6, PP.787-803. DOI:10.1007/s11253-006-0111-8
7. Prykarpatsky Y.A., Samoilenko A.M., The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 1. Opuscula Mathematica, ISSN:1232-9274, 2006, V26, N1, PP.137-150. WebPage:WebPage
2005:
1. Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K. A survey of the spectral and differential generalized de Rham-Hodge theory related with Delsarte transmutation operators in multidimansion and application to spectral and soliton problems. Part 1. Applied Mathematics E-Notes, ISSN:1607-2510, 2005, N5, PP.210-246. WebPage:WebPage
2. Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K. A survey of the spectral and differential generalized de Rham-Hodge theory related with Delsarte transmutation operators in multidimansion and application to spectral and soliton problems. Part 2. Applied Mathematics E-Notes, ISSN:1607-2510, 2005, N6, PP.84-112. WebPage:WebPage
3. Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K. The generalized de Rham-Hodge-Skrypnyk theory: differential-spectral aspects and some applications. Ukrainian Mathematical Bulletin, 2005, V2, N4, PP.550-582 (in Ukrainian)
4. Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K. The de Rham-Hodge theory of Delsarte transmutation operators in multidimension and its applications. Reports on Mathematical Physics, ISSN:0034-4877, 2005, V55, N3, PP.351-370. DOI:10.1016/S0034-4877(05)80051-5
5. Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K. The geometric properties of reduced canonically symplectic spaces with symmetry, their relationship with structures on associated principal fiber bundles and some applications. Part 1. Opuscula Mathematica, ISSN:1232-9274, 2005, V25, N2, PP287-299. WebPage:WebPage
6. Samoilenko A.M., Prykarpatsky Y.A., Prykarpatsky A.K., The generalized de Rham-Hodge theory aspects of Delsarte-Darboux type transformations in multidimension. Central European Journal of Mathematics, 2005, V3, N3, pp.529-557. DOI:10.2478/BF02475922
7. Blackmore D.L., Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K. The ergodic measures related with nonautonomous hamiltonian systems and their homology structure. Part 1. CUBO A Mathematical Journal, 2005, V7, N3, PP.49-64.
8. Prykarpatsky Y.A., Samoilenko A.M., On the Lagrangian and Hamiltonian aspects of infinite-dimensional dynamical systems and their finite-dimensional reductions. Nonlinear Oscillations, ISSN:1536-0059, 2005, V8, N3, PP.360-387. DOI:10.1007/s11072-006-0007-4
9. Bogoliubov N.N., Prykarpatsky Ya.A., Samoilenko A.M., Prykarpatsky A.K., A generalized de Rham-Hodge theory of multidimensional Delsarte transmutations of differential operators and its applications for nonlinear dynamic systems. Physics of Particles and Nuclei, ISSN:1063-7796, 2005, V36, Suppl.1, PP.S110-S121.
10. Prykarpatsky Y., Samoilenko A., Blackmore D.L., Prykarpatsky A.K., Integrability by quadratures of Hamiltonian systems and Picard-Fuchs type equations: The modern differential-geometric aspects. Miskolc Mathematical Notes, ISSN:1787-2405, 2005, V6, N1, P.65-103. DOI:10.18514/MMN.2005.87
11. Golenia J., Prykarpatsky A.K., Prykarpatsky Y.A., The Structure of Gelfand-Levitan-Marchenko Type Equations for Delsarte Transmutation Operators of Linear Multidimensional Differerential Operators and Operator Pencils. Part 2. Journal of Nonlinear Mathematical Physics, ISSN:1402-9251, 2005, V12, N3, P.381-408. DOI:10.2991/jnmp.2005.12.3.5
12. Golenia J., Prykarpatsky A.K., Prykarpatsky Y.A., The Structure of Gelfand-Levitan-Marchenko Type Equations for Delsarte Transmutation Operators of Linear Multidimensional Differerential Operators and Operator Pencils. Part 1. Journal of Nonlinear Mathematical Physics, ISSN:1402-9251, 2005, V12, N1, P.73-87. DOI:10.2991/jnmp.2005.12.1.7
2004:
1. Prykarpatsky Y.A, Samoilenko A.M. The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 2. Apply Problems of Mechanics and Mathematics, Scientific Proceedings, ISSN:1810-3022, 2004, Issue 2, PP.7-30
2. Prykarpatsky Y.A., Samoilenko A.M., The generalized De Rham-Hodge-Skrypnik theory of Delsarte transmutation operators in multidimension and its applications. Nonlinear Oscillations, ISSN:1536-0059, 2004, V7, N4, P.516-537. DOI:10.1007/s11072-005-0029-3
3. Samoilenko A., Prykarpatsky Y., Blackmore D., Prykarpatsky A., On the Liouville-Arnold integrable Flows Related with quantum algebras and their Poissonian representations, Proceed. of the Inst. of Math of NAS of Ukraine, 2004, V.5, Part 3, P.1184-1191.
4. Golenia J., Prykarpatsky Y.A., Samoilenko A.M., Prykarpatsky A.K., The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Opuscula Mathematica, ISSN:1232-9274, 2004, V24, 1, P.71-83. WebPage:WebPage
5. Samoilenko A.M., Prykarpatsky Y.A., Taneri Ufuk, Prykarpatsky A.K., Blackmore D.L., A geometrical approach to quantum holonomic computing algorithms. Mathematics and Computers in Simulations, ISSN:0378-4754, 2004, 66, P.1-20. DOI:10.1016/j.matcom.2004.01.017
6. Samulyak R., Lu T., Prykarpatskyy Y., Direct and homogeneous numerical approaches to multiphase flows and applications, Lecture Notes in Computer Science, ISSN:0302-9743, 2004. V3039. P.653-660. DOI:10.1007/978-3-540-25944-2_84
7. Samulyak R., Prykarpatskyy Y., Richtmyer-Meshkov instability in liquid metal flows: influence of cavitation and magnetic fields, Mathematics and Computers in Simulation, ISSN:0378-4754, 2004, V65, P.431-446. DOI:10.1016/j.matcom.2004.01.019
2003:
1. Prykarpatsky A.K., Samoilenko A.M., Prykarpatsky Y.A., The multidimensional Delsarte transmutation operators, their differential-geometric structure and applications. Part 1. Opuscula Mathematica, ISSN:1232-9274, 2003, V23, P. 71-79. WebPage:WebPage
2. Prykarpatsky Y., Kopych M., On integrability of a hydrodynamical system and its dimensional reductions. Visnyk Lviv Univ., Ser.Mech.-Math., 2003. V.62. P.103-108 WebPage:WebPage
3. Prykarpatsky Y.A., Samoilenko A.M., Samoilenko V.G., The structure of Darboux type binary transformations and their applications in soliton theory. Ukrainian Mathematical Journal, ISSN:0041-5995, 2003. V55, 12, P.1704-1719. DOI:10.1023/B:UKMA.0000031664.23436.5a
2002:
1. Prykarpatskyy Y. Finite dimensional local and nonlocal reductions of one type of hydrodynamic systems. Reports on Mathematical Physics, ISSN:0034-4877, 2002. V50. N3. P349-360. DOI:10.1016/S0034-4877(02)80065-9
2. Prykarpatsky Y. New approach to studing the vortex structure of Josephson media equations within the framework of Chern-Simon-Higgs Lagrangean model. Physica C, ISSN:0921-4534, 2002. V.369. P.325-330. DOI:10.1016/S0921-4534(01)01269-2
2001:
1. Prykarpatsky Ya.A., Prytula M.M., Revenko V.P. About a scalar Lax type representation for one class of hydrodynamic systems in one dimension. Reports of the National Academy of Sciences of Ukraine, ISSN:1025-6415, 2001. N8. PP.49-53
2. Samoilenko A.M.,Prykarpatsky Y.A. The complete integrabilty and Picard-Fuchs equations of a four-dimensional truncated Focker-Plank Hamiltonian system. Part 1. Nonlinear Oscillation, ISSN:1536-0059, 2001, V4, N2, P.264-271. WebPage:WebPage
3. Prykarpatsky Y., Pytel-Kudela M., Samoylenko V. On a Dirac type quantization algorithm for the Neumann-Bogoliubov oscillatory dynamical system. Nonlinear Oscillation, ISSN:1536-0059, 2001. V4. N1 P.106-111. WebPage:WebPage
2000:
1. Prykarpatsky Y.A., Samoilenko A.M. Geometrical generalization of the Poincaré methods for the investigation of Lagrangian manifolds of slowly perturbed Hamiltonian systems in a neighborhood of a hyperbolic singular point. Nonlinear Oscillations, ISSN:1536-0059, 2000, V3, N2, PP.246-255. WebPage:WebPage
2. Prykarpatsky Y.A., Prytula M.M., Hentosh O.E. Finite-dimensional reductions of a generalized Burgers dynamical systems and its integrability. Nonlinear Oscillations, ISSN:1536-0059, 2000. V3. N1. P.95-102. WebPage:WebPage
1999:
1. Prykarpatsky Y.A., Samoilenko A.M., Blackmore D.L., Embedding of integral submanifolds and associated adiabatic invariants of slowly perturbed integrable Hamiltonian systems. Reports on Mathematical Physics, ISSN:0034-4877, 1999. V44. N1-2. -P.171-182. DOI:10.1016/S0034-4877(99)80158-X
2. Samoilenko A.M., Prykarpatsky Y.A., Investigation of invariant deformations of integral manifolds of adiabatically perturbed integrable Hamiltonian systems. Part 1. Ukrainian Mathematical Journal, ISSN:0041-5995, 1999. V51. N10. -P.1379-1390. DOI:10.1007/BF02981688
3. Samoilenko A.M.,Prykarpatsky Y.A., Investigation of invariant deformations of integral manifolds of adiabatically perturbed integrable Hamiltonian systems. Part 2. Ukrainian Mathematical Journal, ISSN:0041-5995, 1999. V51. N11. -P.1513-1528. DOI:10.1007/BF02525274
4. Prykarpatsky Y.A., Samoilenko A.M., Symplectic analysis of the deformation of slowly-perturbed completely integrable Hamiltonian systems and associated adiabatic invariants. Nonlinear Oscillations, ISSN:1536-0059, 1999. V2, N1. -P.83-91. WebPage:WebPage
5. Kubes P., Prykarpatsky A.K., Zagrodzinski J., Prykarpatsky Y.A. A kinetic model of the plasma flow at the magnetic Z-pinch and the plasmoid structure. Part 2. Journal of Physical Studies, ISSN:1027-4642, 1999. V3. N1. PP.42-46. WebPage:WebPage
6. Prykarpatsky Y.A., The structure of integrable Lax flows on nonlocal manifolds: dynamical systems with sources. Journal of Mathematical Sciences, ISSN:1072-3374, 1999. V.96. N2. pp. 3030-3037. DOI:10.1007/BF02169701
1998:
1. Blackmore D.L., Prykarpatsky Y.A., Samulyak R.V. The integrability of Lie-invariant geometric objects generated by ideals in the Grasssmann algebra. Journal of Nonlinear Mathematical Physics, ISSN:1402-9251, 1998. V.5. N1. -P.54-68. DOI:10.2991/jnmp.1998.5.1.6
2. Prykarpatsky Y.A., Blackmore D.L., Hentosh O.J., Geometric structure of Lax-integrable flows on Grassmann manifolds. Collection of works of the Institute of Mathematics of NAS of Ukraine, 1998, p.41-48.
1997:
1. Kopych M., Prykarpatsky Y., Samulyak R. Adiabatic invariants of a generalized Henon-Heiles Hamiltonian system and structure of the chaotic motion. Proceeding of the National Academy of Sciences of Ukraine. 1997. N2. -P.32-36.
2. Prykarpatsky Ya.A. The structure of Lax-type integrable flows on nonlocal manifolds: dynamical systems with sources. Mathematical Methods and Physicomechanical Fields, ISSN:0130-9420, 1997. V.40. N4. -P.106-115. (in Ukrainian)