Roman O. Popovych
Roman POPOVYCH
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Address:
Department of Applied Research
Institute of Mathematics
National Academy of Sciences of Ukraine
3 Tereshchenkivs'ka Street
01601 Kyiv-4
UKRAINE
Phone: +380 (44) 234 63 22 (office)
Fax: +380 (44) 235 2010 (office)
E-mail: rop[at]imath[dot]kiev[dot]ua
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Current address: Fakultät für Mathematik, Nordbergstraße 15, 1090 Wien, Österreich
Office: Nordbergstraße 15, room C 415
Phone: +43 1 4277 50614 (office)
Academic Background:
Associate Professor: 2005, Institute of Mathematics, Kyiv
Ph.D. in Math.: 1992, Institute of Mathematics, Kyiv
M.Sc. in Math.: 1989, Kyiv State University
Professional Experince:
2006-till now
Principal investigator, Lise Meitner project M923-N13,
Department of Mathematics, University of Vienna
1992-till now
Junior Researcher, Researcher, Senior Researcher at the
Department
of Applied Research of the Institute of Mathematics, Kyiv
1989-1992
Post-graduate Student, Institute of Mathematics, Kyiv
(Supervisor Prof. W.I. Fushchych)
Date of Birth: 24.10.1967 (Transcarpation Region, Ukraine)
Nationality: Ukraine
Marital Status: Married, son
Area of Expertise
Symmetry analysis of differential equations and applications, Lie algebras
Awards
Prize of President of Ukraine for Young Scientists (2001)
Lise Meitner project (2005)
Editorial Boards and Organizing Committees
Associate Editor of the refereed online journal SIGMA
''Symmetry, Integrability and Geometry: Methods and Applications''
(2005-till now)
Organization of the First, Second, Third, Fourth, Fifth, Sixth and Seventh International Conferences
''
Symmetry in Nonlinear Mathematical Physics''
(Kyiv, Ukraine, 1995, 1997, 1999, 2001, 2003, 2005, 2007)
Scientific Committee of
Fifth International School and Workshop "QFT and Hamiltonian Systems" (May 20-26, 2006, Calimanesti, Romania)
Referee
Acta Mechanica
Applied Mathematics Letters
Electronic Journal of Differential Equations (EJDE)
Journal of Mathematical Analysis and Applications
Journal of Mathematical Physics
Journal of Nonlinear Mathematical Physics
Journal of Physics A: Mathematical and Theoretical
Mathematical Methods in the Applied Sciences
Nonlinear Dynamics
Nonlinearity
Physics Letters A
Reports on Mathematical Physics
Reviews in Mathematical Physics
Reviewer
Mathematical Review
Mathematical Zenterblatt
Participation at the International Conferences
Fifth International School and Workshop "QFT and Hamiltonian Systems" (May 20-26, 2006, Calimanesti, Romania)
First and Second Workshop ''Group Analysis of Differential Equations - Integrable Systems''
Nicosia, Cyprus (2005, 2006)
IV International Symposium Quantum Theory and Symmetries
(August 15-21, 2005, Varna, Bulgaria)
International Workshop on Nonlinear Partial Differential Equations
(December 5-16, 2004, Tehran, Iran)
International Conference in Modern Group Analysis (MOGRAN X)
(October 24-31, 2004, Larnaca, Cyprus)
11th Reginal Conference on Mathematical Physics and Mathematics
(May 3-6, 2004, Tehran, Iran)
NATO ASI 2003 "Data Fusion for Situation Monitoring, Incident Detection, Alert and Response Management"
(August 18-29, 2003, Tsakhkadzor, Armenia)
10th International Conference on Symmetry Methods in Physics
(August 13-19, 2003, Yerevan, Armenia)
First, Second, Third, Fourth, Fifth and Sixth International Conferences
''Symmetry in Nonlinear Mathematical Physics''
(Kyiv, Ukraine, 1995, 1997, 1999, 2001, 2003, 2005)
Short Scientific Visits
Department of Mathematics and Statistics, University of Cyprus
(Nicosia, Cyprus, 2004, 2005, 2006)
Centre de Recherches Mathematiques, Universite de Montreal
(Monreal, Canada, 2004)
Institute for Studies in Theoretical Physics and Mathematics (IPM)
(Tehran, Iran, 2003, 2004)
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research
(Dubna, Russia, 2003)
PUBLICATIONS
*** Popovych, Roman O. = Popovych, R.O. = Popovych, R. = Popovich, R.E. = Popowych, R.O. =
Popovich, R.O. = Popowych, Roman
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Boyko V.M., Patera J. and Popovych R.O.,
Invariants of solvable Lie algebras with triangular nilradicals and
diagonal nilindependent elements,
arXiv:0706.2465, 17 p.
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Popovych R.O., Kunzinger M. and Ivanova N.M.,
Conservation laws and potential symmetries of linear parabolic equations,
arXiv:0706.0443, 59 p.
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Boyko V.M., Patera J. and Popovych R.O.,
Invariants of triangular Lie algebras with one nilindependent diagonal element,
arXiv:0705.2394, 10 p.
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Boyko V.M., Patera J. and Popovych R.O.,
Invariants of triangular Lie algebras,
J. Phys. A, 2007, V.40, 7557–7572,
arXiv:0704.0937, 16 p.
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Popovych R.O., Kunzinger M. and Eshraghi H. Admissible point transformations of nonlinear Schrödinger equations,
math-ph/0611061, 23 p.
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Ivanova N.M. and Popovych R.O.,
Equivalence of conservation laws and equivalence of potential systems,
Internat. J. Teoret. Phys., in press, 11 p.
(see math-ph/0611032).
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Popovych R.O., Vaneeva O.O. and Sophocleous C.,
Exact solutions of a remarkable fin equation,
Appl. Math. Lett., to appear,
math-ph/0610017, 6 p.
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Vaneeva O.O., Johnpillai A.G., Popovych R.O. and Sophocleous C.,
Group analysis of nonlinear fin equations,
Appl. Math. Lett., to appear,
math-ph/0610006, 6 p.
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Vaneeva O.O., Johnpillai A.G., Popovych R.O. and Sophocleous C.,
Enhanced group analysis and conservation laws of variable coefficient reaction-diffusion equations
with power nonlinearities, J. Math. Anal. Appl., 2007, V.330, 1363-1386
(see math-ph/0605081).
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Popovych R.O., Vaneeva O.O and Ivanova N.M.
Potential nonclassical symmetries and solutions of fast diffusion equation,
Phys. Lett. A, 2007, V.362, 166-173
(see math-ph/0506067).
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Boyko V.M., Patera J. and Popovych R.O.,
Invariants of Lie algebras with fixed structure of nilradicals,
J. Phys. A, 2007, V.40, 113-130
(see math-ph/0606045).
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Nesterenko N. and Popovych R.O.,
Contractions of low-dimensional Lie algebras,
J. Math. Phys., 2006, V.47, 123515, 45 pages
math-ph/0608018, 47 p.
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Popovych R.O.,
Direct methods of construction of conservation laws,
Physics AUC, 2006, V.16 (II), 81-94.
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Popovych R.O.,
Classification of admissible transformations of differential equations,
Collection of Works of Institute of Mathematics, Kyiv, 2006, V.3, N 2, 239-254.
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Popovych R.O.,
No-go theorem on reduction operators of linear second-order parabolic equations,
Collection of Works of Institute of Mathematics, Kyiv, 2006, V.3, N 2, 231-238.
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Boyko V.M., Patera J. and Popovych R.O.,
Computation of invariants of Lie algebras by means of moving frames,
J. Phys. A, 2006, V.39, 5749-5762
(see math-ph/0602046).
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Popovych R.O.,
Normalized classes of nonlinear Schroedinger equations,
Proceedings of the VI International Workshop "Lie theory and its application to physics"
(15-21 August, 2005, Varna, Bulgaria),
Bulg. J. Phys., 2006, V.33 (s2), 211-222.
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Popovych R.O. and Ivanova N.M.
Hierarchy of conservation laws of diffusion-convection equations,
J. Math. Phys., 2005, V.46, 043502 (22 pages)
(see math-ph/0407008).
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Popovych R.O. and Ivanova N.M.
Potential equivalence transformations for nonlinear diffusion-convection equations,
J. Phys. A, 2005, V.38, 3145-3155
(see math-ph/0402066).
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Eshraghi H., Abedini Y. and Popovych R.O.
Effect of external sources on finite time singularity, Physica Scripta, 2005, V.71, N 1, 52-59.
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Ivanova N.M., Popovych R.O. and Eshraghi H.
On symmetry properties of nonlinear Schroedinger equations with potentials,
Proceedings of Third Summer School in Modern Mathematical Physics
(20-31 August, 2004, Zlatibor, Serbia and Montenegro),
Sveske Fiz. Nauka, 2005, V.18(A1), 451-456.
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Ivanova N.M., Popovych R.O. and Sophocleous C.
Conservation laws of variable coefficient diffusion-convection equations,
Proc. of 10th International Conference in Modern Group Analysis (MOGRAN X) (Larnaca, Cyprus, 2004), 2005, 108-115
(see math-ph/0505015).
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Popovych R.O. and Eshraghi H. Admissible point transformations of nonlinear Schrödinger equations,
Proc. of 10th International Conference in Modern Group Analysis (MOGRAN X) (Larnaca, Cyprus, 2004), 2005, 168-176.
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Nesterenko M. and Popovych R.O.
Realizations of real unsolvable low-dimensional Lie algebras,
in Proceedings of the Third Voronoi Conference on Analytic Number Theory and Spatial Tessellations,
Editors H. Syta, A. Yurachkivsky and P. Engel,
Proceedings of Institute of Mathematics, Kyiv, 2005, V.55, 163-168
(see math-ph/0510015).
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Popovych R.O., Ivanova N.M. and Eshraghi H.
Group classification of (1+1)-dimensional Schrödinger equations with potentials and power nonlinearities,
J. Math. Phys., 2004, V.45, N 8, 3049-3057
(see math-ph/0311039).
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Popovych R.O. and Ivanova N.M. New results on group
classification of nonlinear diffusion-convection equations,
J. Phys. A, 2004, V.37, N 30, 7547-7565
(see math-ph/0306035).
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Popovych R.O., Ivanova N.M., Eshraghi H.
Lie symmetries of (1+1)-dimensional cubic Schrödinger equation with potential,
in Proceedings of Fifth International Conference ''Symmetry in Nonlinear Mathematical Physics''
(23-29 June, 2003, Kyiv), Editors A.G. Nikitin, V.M. Boyko, R.O. Popovych and I.A. Yehorchenko,
Proceedings of Institute of Mathematics, Kyiv, 2004, V.50, Part 1, 219-223,
[pdf]
(see math-ph/0310039).
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Popovych R.O., Boyko V.M., Nesterenko M.O. and Lutfullin M.W.
Realizations of real low-dimensional Lie algebras,
J. Phys. A, 2003, V.36, N 26, 7337-7360
(see math-ph/0301029).
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Popovych R. and Boyko V. Differential invariants of
one-parameter group of local transformations: one independent variable,
Nonlinear
Oscilations, 2002, V.5, N 2, 218-223 (in Ukrainian).
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Popovych R. and Boyko V. Differential invariants and
application to Riccati-type systems, in Proceedings of Fourth International
Conference ''Symmetry in Nonlinear Mathematical Physics'' (9-15 July, 2001,
Kyiv), Editors A.G. Nikitin, V.M. Boyko and R.O. Popovych, Proceedings
of Institute of Mathematics, Kyiv, 2002, V.43, Part 1, 184-193 [pdf]
(see math-ph/0112057).
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Lutfullin M. and Popovych R. Realizations of real
4-dimensional solvable decomposable Lie algebras, in Proceedings of Fourth
International Conference ''Symmetry in Nonlinear Mathematical Physics''
(9-15 July, 2001, Kyiv), Editors A.G. Nikitin, V.M. Boyko and R.O. Popovych,
Proceedings
of Institute of Mathematics, Kyiv, 2002, V.43, Part 2, 466-468. [pdf]
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Boyko V. and Popovych R. On differential invariants
in the space of two variables, Proceedings of Ukrainian Acad. of Sci.,
2001, N 5, 7-10 (in Ukrainian).
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Boyko V. and Popovych R. Differential invariants of
one-parameter Lie groups, in Group and Analytic Methods in Mathematical Physics, Proceedings of Institute of Mathematics, Kyiv, 2001, V.36,
51-62 (in Ukrainian). [pdf]
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Popovych R.O. and Cherniha R.M. Complete classification
of Lie symmetries of system of non-linear two-dimensional Laplace equations,
in Group and Analytic Methods in Mathematical Physics, Proceedings
of Institute of Mathematics, Kyiv, 2001, V.36, 212-221. [pdf]
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Popovych R. and Boyko V. On group classification
Galilei invariant equations of second order, in Book of Abstract of Ukrainian
Mathematical Congress (22-24 August, 2001, Kyiv), Kyiv, Institute of Mathematics,
Section 5 (Math. Phys.), 2001, 25-26 (in Ukrainian).
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Nikitin A.G. and Popovych R.O. Group classification
of nonlinear Schrödinger equations, Ukr. Math. J., 2001, V.53,
N 8, 1255-1265 (see math-ph/0301009).
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Popovych R.O. and Yehorchenko I.A. Group classification
of generalized eikonal equations, Ukr. Math. J., 2001, V.53, N 11,
1513-1520 (in Ukrainian).
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Popovych R.O. and Yehorchenko I.A. Group classification
of generalized eikonal equations, math-ph/0112055
(extended and revised version of paper, Ukr. Math. J., 2001, V.53,
N 11).
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Popovych R.O. Equivalence of Q-conditional
symmetries under group of local transformation, in Proceedings of the Third
International Conference ''Symmetry in Nonlinear Mathematical Physics'',
Eds. A. Nikitin and V. Boyko, Proceedings of Institute of Mathematics,
Kyiv, 2000, V.30, Part 1, 184-189 [pdf]
(see math-ph/0208005).
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Popovych R. and Boyko V. Differential invariants of
one-parameter group of local transformation and integration of Riccati
equation, Vestnik Samarskogo gosudarstvennogo universiteta, 2000,
V.18, N 4, 49-56 (in Russian). [ps]
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Popovych G.V. and Popovych R.O. Flows of incompressible
fluids with linear vorticity, J. Appl. Math. Mech., 1999, V.63,
N 3, 369-374. [pdf]
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Zhdanov R.Z., Tsyfra I.M. and Popovych R.O. A precise
definition of reduction of partial differential equations,
J. Math. Anal. Appl., 1999, V.238, N 1, 101-123 (see math-ph/0207023).
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Vasilenko O.F. and Popovych R.O. On class of reducing
operators and solutions of evolution equations, Vestnik PGTU, 1999,
N 8, 269-273 (in Russian).
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Popovych R.O. On a class of
Q-conditional symmetries
and solutions of evolution equations, in Symmetry and Analytic Methods
in Mathematical Physics, Proceedings of Institute of Mathematics,
Kyiv, 1998, V.19, 194-199 (in Ukrainian). [pdf]
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Popovych R.O. and Korneva I.P., On the Q-conditional
symmetry of the linear n-dimensional heat equation, in Symmetry
and analytic methods in mathematical physics, Proceedings of Institute
of Mathematics, Kyiv, 1998, V.19, 200-211 (in Ukrainian). [pdf]
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Popovych G.V. and Popovych R.O. On Navier-Stokes fields
with linear vorticity, Ukr. Math. J., 1997, V.49, N 9, 1223-1229
(in Ukrainian); translation in Ukr. Math. J., 1997, V.49, N 9, 1377-1385.
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Popovych R.O. On reduction and Q-conditional
(nonclassical) symmetry, in Proceedings of the Second International Conference
''Symmetry in Nonlinear Mathematical Physics'' (Kyiv, July 7-13, 1997),
Editors M.I. Shkil', A.G. Nikitin, V.M. Boyko, Kyiv, Institute of Mathematics,
1997, V. 2, 437-443 [pdf]
(see math-ph/0207015).
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Popovych V.O. and Popovych R.O. Solutions of Navier-Stokes
equations represented as sums of exponents, Proceedings of the III International
conference ''Asymptotical and Qualitative Methods in Theory of Nonlinear
Oscillations'' (Kyiv: Acad. Sci. Ukraine, Inst. Math.), 1997, 139-140 (in
Ukrainian).
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Korneva I.P. and Popovych R.O. On compatibility of
system of nonlinear Laplace equation and generalized Hamilton-Jacobi equation,
Proceedings of the VI International conference named acad. M.P. Kravchuk
(Kyiv: National Tech. University of Ukraine), 1997, 220 (in Ukrainian).
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Popovych R.O. and Popovych V.O. On the Navier-Stokes
equation with the additional condition $u_{11}=u_3=0$,
Ukr. Math. J.,
1996, V.48, N 10, 1363-1374 (in Ukrainian); translation in Ukr. Math.
J., 1996, V.48, N 10, 1546-1560.
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Popovych H.V. and Popovych R.O. Solutions of Euler
equations which have linear vorticity, Vestnik PGTU, 1996, N 2,
255-260 (in Russian).
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Popovych R.O. On generalization of potential flows,
Proceedings of the V International conference named acad. M.P. Kravchuk
(Kyiv: National Tech. University of Ukraine), 1996, 352 (in Ukrainian).
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Popovych R.O. On Lie reduction of the Navier-Stokes
equations, J. Nonlinear Math. Phys., 1995, V. 2, N 3-4, 301-311
[pdf].
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Popovych R.O. On the symmetry and exact solutions
of a transport equation, Ukr. Math. J., 1995, V.47, N 1, 121-125
(in Ukrainian); translation in Ukr. Math. J., 1995, V.47, N 1, 142-148.
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Popovych V.O. and Popovych R.O. Exact solutions of
Navier-Stokes equations for shear flows, Akad. Nauk Ukrainy Inst. Mat.
Preprint N 8, 1997, 24 pages (in Ukrainian).
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Fushchych W.I., Popovych R.O. Symmetry reduction and
exact solution of the Navier-Stokes equations. I, J. Nonlinear Math.
Phys., 1994, V. 1, N 1, 75-113 [pdf]
(see math-ph/0207016
or [pdf]).
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Fushchych W.I., Popovych R.O. Symmetry reduction and
exact solution of the Navier-Stokes equations. II, J. Nonlinear Math.
Phys., 1994, V. 1, N 2, 156-188 [pdf]
(see math-ph/0207016
or [pdf]).
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Fushchych W. I., Popovych R.O. and Popovych G.V. Ansätze
of codimension one for the Navier-Stokes field and reduction of the Navier-Stokes
equations, Proceedings of Ukrainian Acad. of Sci., 1994, N 4, 37-44
[pdf].
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Fushchych W.I. and Popovych R.O. Symmetry reduction
and exact solutions of Navier-Stokes equations, Preprint N 7, Kyiv, Institute
of Mathematics, 1993, 56 p.
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Popovych R.O. On solutions of the Navier-Stokes equations
expressed via solutions of the heat equation, in Symmetry Analysis of Equations
of Mathematical Physics, Kyiv, Institute of Mathematics, Editor W.I. Fushchych,
1992, 90-92.
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Fushchych W. I., Shtelen W.M. and Popovych R.O. On
the reduction of Navier-Stokes equations to linear heat equations, Proceedings
of Ukrainian Acad. of Sci., 1992, N 2, 23-30 (in Ukrainian) [pdf].
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Popovych R.O. General solution of Navier-Stokes equations
with an additional condition, Proceedings of Ukrainian Acad. of Sci.,
1992, N 4, 21-24 (in Ukrainian).
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Fushchych W. I. and Popovych R.O. Symmetry reduction
of the Navier-Stokes equations to linear two-dimensional systems of equations,
Proceedings
of Ukrainian Acad. of Sci., 1992, N 8, 29-37 [pdf].
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Fushchych W. I., Shtelen W.M., Serov M.I. and Popovych
R.O. Q-conditional symmetry of the linear heat equation, Proceedings
of Ukrainian Acad. of Sci., 1992, N 12, 28-33 [pdf].
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Popovych R.O., On general solutionsand symmetry of
Navier-Stokes equations with additional condition $(\vec u\cdot\nabla)\vec
u=\vec 0$, Proceedings of the International conference dedicated the memory
of acad. M.P. Kravchuk (Kyiv: Acad. Sci. Ukraine, Inst. Math.), 1992, 163
(in Ukrainian).
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Popovych R.O. Symmetry properties of an integro-differential
equation of Hartree type, in Algebro-Theoretic Analysis of Equations in
Mathematical Physics, Kyiv, Institute of Mathematics, Editor W.I. Fushchych,
1990, 50-53 (in Russian).
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Goncharenko V.M., Popovych R.E., Popovych G.V. and Halikov D.
Method of boundary integral equations in problem on steady-state oscillations of elastic body with cracks,
UkrNIINTI Preprint. N 2684-Uk89, 1989, 27 pages (in Russian).
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Goncharenko V.M., Popovych R.E.
On problem of difraction of plane monochromatic wave on crack of finite length,
UkrNIINTI Preprint. N 2685-Uk89, 1989, 20 pages (in Russian).
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Ayvazova L.S., Goncharenko V.M., Goncharenko M.I. and Popovych R.E.
On heat deformation arising upon laser irradiation of rigid body,
UkrNIINTI Preprint. N 2686-Uk89, 1989, 20 pages (in Russian).
EDITORIAL ACTIVITIES
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Boyko V.M., Nikitin A.G. and Popovych R.O. (Editors), Symmetry and
Integrability of Equations of Mathematical Physics
(Dedicated to the 70-th Anniversary of Professor W.I. Fushchych), Collection of Works of Institute
of Mathematics, Kyiv, 2006, V.3, N 2, 400 pp.
You can download pdf
(1.94 Mb).
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Boyko V.M., Gorbachuk M.L., Lukovs'kyi I.O., Nikitin A.G., Popovych R.O., Samoilenko A.M. (Editors),
W.I.
Fushchych, Selected Works, Kyiv, Naukova Dumka, 2005, 448 pp.
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Nikitin A.G., Boyko V.M., Popovych R.O. and Yehorchenko I.A. (Editors),
Proceedings
of Fifth International Conference ''Symmetry in Nonlinear Mathematical
Physics'' (23-29 June, 2003, Kyiv), Proceedings of Institute of
Mathematics, Kyiv, 2004, V.50, Parts 1-3, 1528 pp.
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Nikitin A.G., Boyko V.M. and Popovych R.O. (Editors),
Proceedings
of Fourth International Conference ''Symmetry in Nonlinear Mathematical
Physics'' (9-15 July, 2001, Kyiv), Proceedings of Institute of Mathematics,
Kyiv, 2002, V.43, Parts 1-2, 784 pp.
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Boyko V.M., Lykova O.B., Popovych R.O. and Pustovoitov M.O. (Editors), Outlines of History of Mathematics and Mathematical Sciences
(on the Occasion of Ninetieth Birthday of O.M. Bogolyubov), Proceedings
of Institute of Mathematics, Kyiv, 2001, V.39, 160 pp.
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Boyko V.M., Nikitin A.G. and Popovych R.O. (Editors),
Group and Analytic Methods in Mathematical Physics, Proceedings of Institute
of Mathematics, Kyiv, 2001, V.36, 324 pp. You can download pdf
(1.63 Mb) or pdf-booklet
(1.53 Mb).
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Bogolyubov O.M., Popovych R.O. and Pustovoitov M.O. (Editors),
Mathematics and the Mathematical Sciences in Ukraine in the Twentieth Century
(Proceedings of the International Summer Scientific School held in Kam'yanets'-Podil's'kii, July 1-7, 1999),
Proceedings of Institute of Mathematics, Kyiv, 2001, V.34, 240 pp.
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Nikitin A.G., Lopatin O.K., Boyko V.M., Zhdanov R.Z.,
Popovych R.O. and Cherniha R.M. (Editors), Symmetry and Analytic Methods
in Mathematical Physics, Proceedings of Institute of Mathematics,
Kyiv, 1998, V.19, 280 pp. You can download pdf
(1.35 Mb) or pdf-booklet
(1.27 Mb).
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Bogolyubov O.M., Vyvrot T.M., Koshlyakov V.M., Pustovoitov M.O. and Popovych R.O. (Editors),
The Institute of Mathematics. Outlines of Its Development,
Proceedings of Institute of Mathematics, Kyiv, 1997, V.17, 248 pp.