Roman POPOVYCH

           
Address:
Department of Applied Research
Institute of Mathematics
National Academy of Sciences of Ukraine
3 Tereshchenkivs'ka Street
01004 Kyiv
UKRAINE

Phone: +380 (44) 234 63 22 (office)
Fax: +380 (44) 235 2010 (office)
E-mail: rop[at]imath[dot]kiev[dot]ua
ORCID: orcid.org/0000-0003-2403-1525
ResearcherID: I-8056-2012

Current address: Wolfgang Pauli Institute, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
Office: Oskar-Morgenstern-Platz 1, room 03.133
Phone: +43 1 4277 50632 (office)
Fax: +43 1 4277 50620

Academic Background:
D.Sc. in Math.: 2009, Institute of Mathematics, NAS of Ukraine, Kyiv (Consultant Prof. A.M. Samoilenko)
Associate Professor: 2005, Institute of Mathematics, NAS of Ukraine, Kyiv
Ph.D. in Math.: 1992, Institute of Mathematics, NAS of Ukraine, Kyiv (Supervisor Prof. W.I. Fushchych)
M.Sc. in Math.: 1989, Taras Shevchenko Kyiv State University (Supervisor Prof. W.I. Fushchych)

Professional Experience:
2013-till now
Principal investigator, Stand-alone project P25064 of FWF, Wolfgang Pauli Institute, Vienna
2008-2013
Principal investigator, Stand-alone project P20632 of FWF, Department of Mathematics, University of Vienna, and Wolfgang Pauli Institute, Vienna
2006-2008
Principal investigator, Lise Meitner project, Department of Mathematics, University of Vienna
1992-till now
Junior Researcher, Researcher, Senior Researcher, Leading Researcher at the Department of Applied Research, Institute of Mathematics, NAS of Ukraine, Kyiv
1989-1992
PhD Student, Institute of Mathematics, Kyiv

Area of Expertise
Symmetry analysis of differential equations and applications, Lie algebras

Awards and Grants
Stand-alone project P25064 of FWF (2013)
Stand-alone project P20632 of FWF (2008)
Lise Meitner project M923-N13 of FWF (2005)
Prize of President of Ukraine for Young Scientists (2001)

Former PhD Students
Elsa Maria Dos Santos Cardoso-Bihlo, thesis: "Group analysis and invariant parameterization in dynamic meteorology" (2014), University of Vienna
Alexander Bihlo (jointly with Prof. M. Hantel), thesis: "Symmetry methods in the atmospheric sciences" (2010), University of Vienna
Olena Vaneeva, thesis: "Group classification and nonclassical symmetries of reaction–diffusion equations" (2008), Institute of Mathematics, NAS of Ukraine, Kyiv
Maryna Nesterenko (jointly with Prof. A.G. Nikitin), thesis: "Contractions and realizations of Lie algebras" (2007), Institute of Mathematics, NAS of Ukraine, Kyiv
Maxim Lutfullin (jointly with Prof. A.G. Nikitin), thesis: "Realizations of low-dimensional Lie algebras and invariant systems of nonlinear differential equations" (2005), Institute of Mathematics, NAS of Ukraine, Kyiv

Former Master Students
Célestin Kurujyibwami (jointly with Prof. P. Basarab-Horwath), Group classification of linear Schrödinger equations by the algebraic method, Licentiate Thesis, Linköping Studies in Science and Technology. Thesis No. 1743, Linköping University, 2016.

Editorial Boards and Organizing Committees
Associate Editor of the Journal of Mathematical Analysis and Applications (2009-till now)
Associate Editor of the refereed online journal SIGMA ''Symmetry, Integrability and Geometry: Methods and Applications'' (2005-till now)
Member of Local Organizing Committee of the International Conference Series
'' Symmetry in Nonlinear Mathematical Physics'' (1995, 1997, 1999, 2001, 2003, 2005, 2007, 2009, Kyiv, Ukraine)
Member of Organizing Committee of the International Workshop Series ''Group Analysis of Differential Equations and Integrable Systems'' (2005, 2006, 2007, 2008, 2010, 2012, 2014, Cyprus)
Member of Scientific Committee of the 11th and 12th Conferences ''Mathematics in Technical and Natural Sciences'' (8-12 September 2010 and 4-10 September 2011, Krynica, Poland)
Member of Organizing Committee of the International Workshop ''Symmetries and integrability of equations of mathematical physics'' in honor of Professor Wilhelm Fushchych (18-19 December 2011, Kyiv, Ukraine)
Member of Scientific Committee of the Fifth International School and Workshop "QFT and Hamiltonian Systems" (20-26 May 2006, Calimanesti, Romania)

Referee
Acta Applicandae Mathematicae
Acta Mechanica
Applied Mathematics Letters
Electronic Journal of Differential Equations (EJDE)
IMA Journal of Applied Mathematics
Journal of Engineering Mathematics
Journal of Mathematical Analysis and Applications
Journal of Mathematical Physics
Journal of Nonlinear Mathematical Physics
Journal of Physics A: Mathematical and Theoretical
manuscripta mathematica
Mathematical Methods in the Applied Sciences
Modern Physics Letters B
Nonlinear Analysis A: Theory and Methods
Nonlinear Dynamics
Nonlinearity
Physics Letters A
Proceedings of Royal Society A
Reports on Mathematical Physics
Reviews in Mathematical Physics
etc.

Reviewer
Mathematical Review
Mathematical Zenterblatt

Participation at International Conferences and Workshops
''Workshop on Integrable Nonlinear Equations'' (18-24 October 2015, Mikulov, Czech Republic)
International Workshop Series ''Group Analysis of Differential Equations and Integrable Systems''
(27 October 2005; 25-28 September 2006; 4-5 October 2007; Nicosia, Cyprus; 26-30 October 2008; 6-10 June 2010; 17-21 June 2012; Protaras, Cyprus; 15-19 June 2014, Larnaka, Cyprus)
International Workshop ''Symmetries and integrability of equations of mathematical physics'' in honor of Professor Wilhelm Fushchych (18-19 December 2011; 21-24 December 2013; Kyiv, Ukraine)
''2012 Canadian Mathematical Society (CMS) Winter Meeting, Session ''Symmetries of Differential and Difference Equations'' (8-9 December 2012, Montréal, Canada)
11th and 12th Conferences ''Mathematics in Technical and Natural Sciences'' (8-12 September 2010 and 4-10 September 2011, Krynica, Poland)
International Conference Series ''Symmetry in Nonlinear Mathematical Physics''
(3-8 July 1995; 7-13 July 1997; 12-18 July 1999; 9-15 July 2001; 23-29 June 2003; 20-26 June 2005; 24-30 June 2007; 21-27 June 2009; Kyiv, Ukraine)
Applications of Computer Algebra (ACA2008), the session Symbolic Symmetry Analysis and Its Applications (27-30 July 2008, RISC, Castle of Hagenberg, Austria)
MM-VII Symmetries and Mechanics Conference (24-27 September 2007, Novi Sad, Serbia)
Fifth International School and Workshop "QFT and Hamiltonian Systems" (20-26 May 2006, Calimanesti, Romania)
IV International Symposium Quantum Theory and Symmetries (15-21 August 2005, Varna, Bulgaria)
International Workshop on Nonlinear Partial Differential Equations (5-16 December 2004, Tehran, Iran)
International Conference in Modern Group Analysis (MOGRAN X) (24-31 October 2004, Larnaca, Cyprus)
11th Regional Conference on Mathematical Physics and Mathematics (3-6 May 2004, Tehran, Iran)
NATO ASI 2003 "Data Fusion for Situation Monitoring, Incident Detection, Alert and Response Management" (18-29 August 2003, Tsakhkadzor, Armenia)
10th International Conference on Symmetry Methods in Physics (13-19 August 2003, Yerevan, Armenia)

Invited Scientific Visits
Department of Mathematics and Statistics, University of Saskatchewan (Saskatoon, Canada, 10-15 June 2013; 2-16 November 2014; 2-17 September 2015)
Department of Mathematics and Statistics, University of Cyprus (Nicosia, Cyprus, 2004, 2005, 2006, 2007, 2008, 2010; 29 September - 15 October 2013; 24 September - 11 October 2015)
Mathematical Institute in Opava, Silesian University in Opava (Opava, Czech Republic, 6-20 October 2014; 11-22 May 2015)
Department of Mathematics, Linköping University, (Linköping, Sweden, 3-29 November 2013; 21-27 February 2016)
Department of Mathematics and Statistics, McGill University (Montréal, Canada, 23-29 April 2013)
Faculty of Engineering, Katholieke Universiteit Leuven, Campus Kortrijk (Belgium, Kortrijk, 28 May - 1 June 2012)
Centre de Recherches Mathématiques, Universite de Montréal (Montréal, Canada, 2004)
Institute for Studies in Theoretical Physics and Mathematics (IPM) (Tehran, Iran, 6 September - 22 October, 2003; 26 April - 24 May 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. = Popovich, R.Y. = Popovich, R.Ye. = Popowych, R.O. = Popovich, R.O. = Popowych, Roman

  1. Bihlo A. and Popovych R.O., Group classification of linear evolution equations, arXiv:1605.09251, 24 pp.
  2. Pocheketa O.A. and Popovych R.O., Extended symmetry analysis of generalized Burgers equations, arXiv:1603.09377, 31 pp.
  3. Bihlo A., Dos Santos Cardoso-Bihlo E. and Popovych R.O., Invariant and conservative parameterization schemes, Chapter 28 in Parameterization of Atmospheric Convection. Vol. 2. Current Issues and New Theories, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2015, pp. 483-524.
  4. Bihlo A., Dos Santos Cardoso-Bihlo E.M. and Popovych R.O., Algebraic method for finding equivalence groups, J. Phys.: Conf. Ser. 621 (2015) 012001, 17 pp., arXiv:1503.06487.
  5. Boyko V.M., Popovych R.O. and Shapoval N.M., Equivalence groupoids of classes of linear ordinary differential equations and their group classification, J. Phys.: Conf. Ser. 621 (2015) 012002, 17 pp., arXiv:1403.6062.
  6. Vaneeva O.O., Popovych R.O. and Sophocleous C., Group analysis of Benjamin–Bona–Mahony equations with time dependent coefficients, J. Phys.: Conf. Ser. 621 (2015) 012016, 13 pp. arXiv:1506.08137.
  7. Dos Santos Cardoso-Bihlo E.M. and Popovych R.O., On the ineffectiveness of constant rotation in the primitive equations and their symmetry analysis, arXiv:1503.04168, 15 pp.
  8. Pocheketa O.A., Popovych R.O. and Vaneeva O.O., Group classification and exact solutions of variable-coefficient generalized Burgers equations with linear damping, Appl. Math. Comput. 243 (2014) 232–244, arXiv:1308.4265.
  9. Vaneeva O.O., Popovych R.O. and Sophocleous C., Equivalence transformations in the study of integrability, Phys. Scr. 89 (2014), 038003, 9 pp., arXiv:1308.5126.
  10. Bihlo A., Dos Santos Cardoso-Bihlo E. and Popovych R.O., Invariant parameterization and turbulence modeling on the beta-plane, Phys. D 269 (2014), 48-62, arXiv:1112.1917.
  11. Dos Santos Cardoso-Bihlo E. and Popovych R.O., Complete point symmetry group of the barotropic vorticity equation on a rotating sphere, J. Engrg. Math. 82 (2013), 31-38, arXiv:1206.6919.
  12. Pocheketa O.A. and Popovych R.O., Reduction operators of Burgers equation, J. Math. Anal. Appl. 398 (2013), 270-277, arXiv:1208.0232.
  13. Boyko V.M., Popovych R.O. and Shapoval N.M., Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients, J. Math. Anal. Appl. 397 (2013), 434-440, arXiv:1203.0387.
  14. Boyko V.M. and Popovych R.O., Reduction operators of the linear rod equation, Proceedings of the Sixth International Workshop "Group Analysis of Differential Equations and Integrable Systems" (Protaras, Cyprus, June 17-21, 2012), University of Cyprus, Nicosia, 2013, 17-29.
  15. Vaneeva O.O., Popovych R.O. and Sophocleous C., Group classification of the Fisher equation with time-dependent coefficients, Proceedings of the Sixth International Workshop "Group Analysis of Differential Equations and Integrable Systems" (Protaras, Cyprus, June 17-21, 2012), University of Cyprus, Nicosia, 2013, 225-237.
  16. Bihlo A. and Popovych R.O., Invariant discretization schemes for the shallow-water equations, SIAM J. Sci. Comput. 34 (2012), no. 6, B810-B839, arXiv:1201.0498.
  17. Bihlo A., Dos Santos Cardoso-Bihlo E. and Popovych R.O., Complete group classification of a class of nonlinear wave equations, J. Math. Phys. 53 (2012), 123515, 32 pp., arXiv:1106.4801.
  18. Pocheketa O.A. and Popovych R.O., Reduction operators and exact solutions of generalized Burgers equations, Phys. Lett. A 376 (2012), 2847-2850, arXiv:1112.6394.
  19. Popovych R.O. and Bihlo A., Symmetry preserving parameterization schemes, J. Math. Phys. 53 (2012), 073102, 36 pp., arXiv:1010.3010.
  20. Vaneeva O.O., Popovych R.O. and Sophocleous C., Extended group analysis of variable coefficient reaction-diffusion equations with exponential nonlinearities, J. Math. Anal. Appl. 396 (2012), 225-242, arXiv:1111.5198.
  21. Bihlo A. and Popovych R.O., Lie reduction and exact solutions of vorticity equation on rotating sphere, Phys. Lett. A 376 (2012), 1179-1184, arXiv:1112.3019.
  22. Boyko V.M., Kunzinger M. and Popovych R.O., Singular reduction modules of differential equations, arXiv:1201.3223, 30 pp.
  23. Kunzinger M. and Popovych R.O., Generalized conditional symmetries of evolution equations, J. Math. Anal. Appl. 379 (2011), 444-460, arXiv:1011.0277.
  24. Bihlo A. and Popovych R.O., Lie symmetry analysis and exact solutions of the quasi-geostrophic two-layer problem, J. Math. Phys. 52 (2011), 033103, 24 pp., arXiv:1010.1542.
  25. Dos Santos Cardoso-Bihlo E., Bihlo A. and Popovych R.O., Enhanced preliminary group classification of a class of generalized diffusion equations, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), 3622-3638, arXiv:1012.0297.
  26. Vaneeva O.O., Popovych R.O. and Sophocleous C., Reduction operators of variable coefficient semilinear diffusion equations with an exponential source, Proceedings of 5th Workshop "Group Analysis of Differential Equations and Integrable Systems" (June 6-10, 2010, Protaras, Cyprus), 2011, 207-219, arXiv:1010.2046.
  27. Bihlo A. and Popovych R.O., Point symmetry group of the barotropic vorticity equation, Proceedings of 5th Workshop "Group Analysis of Differential Equations and Integrable Systems" (June 6-10, 2010, Protaras, Cyprus), 2011, 15-27, arXiv:1009.1523.
  28. Boyko V.M. and Popovych R.O., Simplest potential conservation laws of linear evolution equations, Proceedings of 5th Workshop "Group Analysis of Differential Equations and Integrable Systems" (June 6-10, 2010, Protaras, Cyprus), 2011, 28-39, arXiv:1008.4851.
  29. Popovych D.R. and Popovych R.O., Lowest dimensional example on non-universality of generalized Inönü-Wigner contractions, J. Algebra 324 (2010), 2742-2756, arXiv:0812.1705.
  30. Popovych R.O. and Sergyeyev A., Conservation laws and normal forms of evolution equations, Phys. Lett. A 374 (2010), 2210-2217, arXiv:1003.1648.
  31. Popovych R.O. and Vaneeva O.O., More common errors in finding exact solutions of nonlinear differential equations. I, Commun. Nonlinear Sci. Numer. Simul. 15 (2010), 3887-3899, arXiv:0911.1848.
  32. Ivanova N.M., Popovych R.O. and Sophocleous C., Group analysis of variable coefficient diffusion-convection equations. I. Enhanced group classification, Lobachevskii J. Math. 31 (2010), 100-122, arXiv:0710.2731.
  33. Popovych R.O., Kunzinger M. and Eshraghi H., Admissible transformations and normalized classes of nonlinear Schrödinger equations, Acta Appl. Math. 109 (2010), 315-359, arXiv:math-ph/0611061.
  34. Bihlo A. and Popovych R.O., Symmetry justification of Lorenz maximum simplification, Nonlinear Dynam. 61 (2010), 101-107, arXiv:0805.4061.
  35. Bihlo A. and Popovych R.O., Lie symmetries and exact solutions of barotropic vorticity equation, J. Math. Phys. 50 (2009), 123102, 12 pp., arXiv:0902.4099.
  36. Popovych D.R. and Popovych R.O., Equivalence of diagonal contractions to generalized IW-contractions with integer exponents, Linear Algebra Appl. 431 (2009), 1096-1104, arXiv:0812.4667.
  37. Bihlo A. and Popovych R.O., Symmetry analysis of barotropic potential vorticity equation, Commun. Theor. Phys. 52 (2009), 697-700, arXiv:0811.3008.
  38. Vaneeva O.O., Popovych R.O. and Sophocleous C., Enhanced group analysis and exact solutions of variable coefficient semilinear diffusion equations with a power source, Acta Appl. Math. 106 (2009), 1-46, arXiv:0708.3457.
  39. Ivanova N.M., Popovych R.O., Sophocleous C. and Vaneeva O.O., Conservation laws and potential symmetries for certain evolution equations, Physica A 388 (2009), 343-356, arXiv:0806.1698.
  40. Boyko V.M., Patera J. and Popovych R.O., Invariants of Lie Algebras via Moving Frames, Proceedings of 4th Workshop "Group Analysis of Differential Equations and Integrable Systems" (26-30 October 2008, Protaras, Cyprus), 2009, 36-44, arXiv:0904.4462.
  41. Vaneeva O.O., Popovych R.O. and Sophocleous C., Reduction operators of variable coefficient semilinear diffusion equations with a power source, Proceedings of 4th Workshop "Group Analysis of Differential Equations and Integrable Systems" (26-30 October 2008, Protaras, Cyprus), 2009, 191-209, arXiv:0904.3424.
  42. Kunzinger M. and Popovych R.O., Is a nonclassical symmetry a symmetry?, Proceedings of 4th Workshop "Group Analysis of Differential Equations and Integrable Systems" (26-30 October 2008, Protaras, Cyprus), 2009, 107-120, arXiv:0903.0821.
  43. Kunzinger M. and Popovych R.O., Singular reduction operators in two dimensions, J. Phys. A 41 (2008), 505201, 24 pp., arXiv:0808.3577.
  44. Kunzinger M. and Popovych R.O., Potential conservation laws, J. Math. Phys. 49 (2008), 103506, 34 pp., arXiv:0803.1156.
  45. Popovych R.O. and Samoilenko A.M., Local conservation laws of second-order evolution equations, J. Phys. A 41 (2008), 362002, 11 pp., arXiv:0806.2765.
  46. Popovych R.O., Reduction operators of linear second-order parabolic equations, J. Phys. A 41 (2008), 185202, 31 pp., arXiv:0712.2764.
  47. Rajaee L., Eshraghi H. and Popovych R.O., Multi-dimensional quasi-simple waves in weakly dissipative flows, Physica D 237 (2008), 405-419.
  48. Boyko V.M., Patera J. and Popovych R.O., Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements, Linear Algebra Appl. 428 (2008), 834-854, arXiv:0706.2465.
  49. Popovych R.O., Kunzinger M. and Ivanova N.M., Conservation laws and potential symmetries of linear parabolic equations, Acta Appl. Math. 100 (2008), 113-185, arXiv:0706.0443.
  50. Popovych R.O., Vaneeva O.O. and Sophocleous C., Exact solutions of a remarkable fin equation, Appl. Math. Lett. 21 (2008), 209-214, arXiv:math-ph/0610017.
  51. Vaneeva O.O., Johnpillai A.G., Popovych R.O. and Sophocleous C., Group analysis of nonlinear fin equations, Appl. Math. Lett. 21 (2008), 248-253, arXiv:math-ph/0610006.
  52. Boyko V.M., Patera J. and Popovych R.O., Invariants of triangular Lie algebras with one nilindependent diagonal element, J. Phys. A 40 (2007), 9783-9792, arXiv:0705.2394.
  53. Boyko V.M., Patera J. and Popovych R.O., Invariants of triangular Lie algebras, J. Phys. A 40 (2007), 7557–7572, arXiv:0704.0937.
  54. Ivanova N.M. and Popovych R.O., Equivalence of conservation laws and equivalence of potential systems, Internat. J. Theoret. Phys. 46 (2007), 2658-2668, arXiv:math-ph/0611032.
  55. 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. 330 (2007), 1363-1386, arXiv:math-ph/0605081.
  56. Popovych R.O., Vaneeva O.O and Ivanova N.M., Potential nonclassical symmetries and solutions of fast diffusion equation, Phys. Lett. A 362 (2007), 166-173, arXiv:math-ph/0506067.
  57. Boyko V.M., Patera J. and Popovych R.O., Invariants of Lie algebras with fixed structure of nilradicals, J. Phys. A 40 (2007), 113-130, arXiv:math-ph/0606045.
  58. Nesterenko M. and Popovych R.O., Contractions of low-dimensional Lie algebras, J. Math. Phys. 47 (2006), 123515, 45 pp., arXiv:math-ph/0608018.
  59. Popovych R.O., Direct methods of construction of conservation laws, Physics AUC 16(II) (2006), 81-94.
  60. Popovych R.O., Classification of admissible transformations of differential equations, Collection of Works of Institute of Mathematics, Kyiv, 3 (2006), no. 2, 239-254.
  61. Popovych R.O., No-go theorem on reduction operators of linear second-order parabolic equations, Collection of Works of Institute of Mathematics, Kyiv, 3 (2006), no. 2, 231-238.
  62. Boyko V.M., Patera J. and Popovych R.O., Computation of invariants of Lie algebras by means of moving frames, J. Phys. A 39 (2006), 5749-5762, arXiv:math-ph/0602046.
  63. Popovych R.O., Normalized classes of nonlinear Schrödinger equations, Proceedings of the VI International Workshop "Lie theory and its application to physics" (15-21 August, 2005, Varna, Bulgaria), Bulg. J. Phys. 33(s2) (2006), 211-222.
  64. Popovych R.O. and Ivanova N.M., Hierarchy of conservation laws of diffusion-convection equations, J. Math. Phys. 46 (2005), 043502, 22 pp., arXiv:math-ph/0407008.
  65. Popovych R.O. and Ivanova N.M., Potential equivalence transformations for nonlinear diffusion-convection equations, J. Phys. A 38 (2005), 3145-3155, arXiv:math-ph/0402066.
  66. Eshraghi H., Abedini Y. and Popovych R.O., Effect of external sources on finite time singularity, Physica Scripta 71 (2005), 52-59.
  67. Ivanova N.M., Popovych R.O. and Eshraghi H., On symmetry properties of nonlinear Schrödinger equations with potentials, Proceedings of Third Summer School in Modern Mathematical Physics (20-31 August, 2004, Zlatibor, Serbia and Montenegro), Sveske Fiz. Nauka 18(A1) (2005), 451-456.
  68. 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, 107-113, arXiv:math-ph/0505015.
  69. 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, 167-174.
  70. 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 55 (2005), 163-168, arXiv:math-ph/0510015.
  71. 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. 45 (2004), no. 8, 3049-3057, arXiv:math-ph/0311039.
  72. Popovych R.O. and Ivanova N.M., New results on group classification of nonlinear diffusion-convection equations, J. Phys. A 37 (2004), no. 30, 7547-7565, arXiv:math-ph/0306035.
  73. 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 50 (2004), Part 1, 219-223, [pdf], arXiv:math-ph/0310039.
  74. Popovych R.O., Boyko V.M., Nesterenko M.O. and Lutfullin M.W., Realizations of real low-dimensional Lie algebras, J. Phys. A 36 (2003), no. 26, 7337-7360, arXiv:math-ph/0301029v3.
  75. Popovych R.O., Boyko V.M., Nesterenko M.O. and Lutfullin M.W., Realizations of real low-dimensional Lie algebras, arXiv:math-ph/0301029v7, 39 pp. (extended and revised version of paper J. Phys. A 36 (2003), no. 26, 7337-7360).
  76. Popovych R. and Boyko V., Differential invariants of one-parameter group of local transformations: one independent variable, Nonlinear Oscilations 5 (2002), no. 2, 218-223 (in Ukrainian).
  77. 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 43 (2002), Part 1, 184-193 [pdf], arXiv:math-ph/0112057.
  78. 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 43 (2002), Part 2, 466-468. [pdf]
  79. Boyko V. and Popovych R., On differential invariants in the space of two variables, Dopov. Nats. Akad. Nauk Ukr., 2001, no. 5, 7-10 (in Ukrainian).
  80. 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 36 (2001), 51-62 (in Ukrainian). [pdf]
  81. 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 36 (2001), 212-221. [pdf]
  82. 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).
  83. Nikitin A.G. and Popovych R.O., Group classification of nonlinear Schrödinger equations, Ukr. Math. J. 53 (2001), no. 8, 1255-1265, arXiv:math-ph/0301009.
  84. Popovych R.O. and Yehorchenko I.A., Group classification of generalized eikonal equations, Ukr. Math. J. 53 (2001), no. 11, 1513-1520.
  85. Popovych R.O. and Yehorchenko I.A., Group classification of generalized eikonal equations, arXiv:math-ph/0112055, 14 pp. (extended and revised version of paper Ukr. Math. J. 53 (2001), no. 11, 1513-1520).
  86. Popovych R. and Boyko V., Differential invariants of one-parameter group of local transformation and integration of Riccati equation, Vestnik Samarskogo gosudarstvennogo universiteta 18 (2001), no. 4, 49-56 (in Russian). [pdf]
  87. 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 30 (2000), Part 1, 184-189 [pdf], arXiv:math-ph/0208005.
  88. Popovych G.V. and Popovych R.O., Flows of incompressible fluids with linear vorticity, J. Appl. Math. Mech. 63 (1999), no. 3, 369-374. [pdf]
  89. Zhdanov R.Z., Tsyfra I.M. and Popovych R.O., A precise definition of reduction of partial differential equations, J. Math. Anal. Appl. 238 (1999), no. 1, 101-123, arXiv:math-ph/0207023.
  90. Vasilenko O.F. and Popovych R.O., On class of reducing operators and solutions of evolution equations, Vestnik PGTU, 1999, no. 8, 269-273 (in Russian).
  91. 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 19 (1998), 194-199 (in Ukrainian). [pdf]
  92. 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 19 (1998), 200-211 (in Ukrainian). [pdf]
  93. Popovych G.V. and Popovych R.O., On Navier-Stokes fields with linear vorticity, Ukr. Math. J. 49 (1997), no. 9, 1223-1229 (in Ukrainian); translation in Ukr. Math. J. 49 (1997), no. 9, 1377-1385.
  94. 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, 2 (1997), 437-443  [pdf], arXiv:math-ph/0207015.
  95. 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).
  96. 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).
  97. Popovych R.O. and Popovych V.O., On the Navier-Stokes equation with the additional condition u^1_1=u^3=0, Ukr. Math. J. 48 (1996), no. 10, 1363-1374 (in Ukrainian); translation in Ukr. Math. J. 48 (1996), no. 10, 1546-1560.
  98. Popovych H.V. and Popovych R.O., Solutions of Euler equations which have linear vorticity, Vestnik PGTU, 1996, no. 2, 255-260 (in Russian).
  99. 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).
  100. Popovych R.O., On Lie reduction of the Navier-Stokes equations, J. Nonlinear Math. Phys. 2 (1995), no. 3-4, 301-311 [pdf].
  101. Popovych R.O., On the symmetry and exact solutions of a transport equation, Ukr. Math. J. 47 (1995), no. 1, 121-125 (in Ukrainian); translation in Ukr. Math. J. 47 (1995), no. 1, 142-148.
  102. Popovych V.O. and Popovych R.O., Exact solutions of Navier-Stokes equations for shear flows, Akad. Nauk Ukrainy Inst. Mat. Preprint no. 8, 1995, 24 pages (in Ukrainian).
  103. Fushchych W.I., Popovych R.O., Symmetry reduction and exact solutions of the Navier-Stokes equations. I, J. Nonlinear Math. Phys. 1 (1994), no. 1, 75-113 [pdf], arXiv:math-ph/0207016 or [pdf].
  104. Fushchych W.I., Popovych R.O., Symmetry reduction and exact solutions of the Navier-Stokes equations. II, J. Nonlinear Math. Phys. 1 (1994), no. 2, 158-188 [pdf], arXiv:math-ph/0207016 or [pdf].
  105. 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, Dopov. Nats. Akad. Nauk Ukr., 1994, no. 4, 37-44 [pdf].
  106. Fushchych W.I. and Popovych R.O., Symmetry reduction and exact solutions of Navier-Stokes equations, Preprint no. 7, Kyiv, Institute of Mathematics, 1993, 56 p.
  107. 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.
  108. Fushchych W. I., Shtelen W.M. and Popovych R.O., On the reduction of Navier-Stokes equations to linear heat equations, Dopov. Nats. Akad. Nauk Ukr., 1992, no. 2, 23-30 (in Ukrainian) [pdf].
  109. Popovych R.O., General solution of Navier-Stokes equations with an additional condition, Dopov. Nats. Akad. Nauk Ukr., 1992, no. 4, 21-24 (in Ukrainian).
  110. Fushchych W.I. and Popovych R.O., Symmetry reduction of the Navier-Stokes equations to linear two-dimensional systems of equations, Dopov. Nats. Akad. Nauk Ukr., 1992, no. 8, 29-37 [pdf].
  111. Fushchych W.I., Shtelen W.M., Serov M.I. and Popovych R.O., Q-conditional symmetry of the linear heat equation, Dopov. Nats. Akad. Nauk Ukr., 1992, no. 12, 28-33 [pdf].
  112. 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).
  113. 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, 1990, 50-53 (in Russian).
  114. 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. no. 2684-Uk89, 1989, 27 pages (in Russian).
  115. Goncharenko V.M., Popovych R.E., On problem of difraction of plane monochromatic wave on crack of finite length, UkrNIINTI Preprint. no. 2685-Uk89, 1989, 20 pages (in Russian).
  116. 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. no. 2686-Uk89, 1989, 20 pages (in Russian).
EDITORIAL ACTIVITIES
  1. Vaneeva O.O., Sophocleous C., Popovych R.O., Boyko V.M. and Damianou P.A. (Eds.), Seventh International Workshop: Group Analysis of Differential Equations and Integrable Systems (GADEIS VII) 15–19 June 2014, Larnaca, Cyprus, J. Phys.: Conf. Ser. 621 (2015).
  2. Maharaj S.D., Moyo S., Popovych R. (Eds.), Special issue on the tercentenary of the Laplace–Runge–Lenz vector, J. Engrg. Math. 82 (2013) issue 1.
  3. Vaneeva O.O., Sophocleous C., Popovych R.O., Leach P.G.L., Boyko V.M. and Damianou P.A. (Eds.), Proceedings of the Sixth International Workshop Group Analysis of Differential Equations and Integrable Systems" (Protaras, Cyprus, June 17-21, 2012), University of Cyprus, Nicosia, 2013, 248 pp.
  4. N.M. Ivanova, Leach P.G.L., Popovych R.O., Sophocleous C. and Damianou P.A. (Editors), Proceedings of 5th Workshop "Group Analysis of Differential Equations and Integrable Systems" (Protaras, Cyprus, June 6-10, 2010), University of Cyprus, Nicosia, 2011, 240 pp.
  5. Ivanova N.M., Popovych R.O., Sophocleous C., Damianou P. and Nikitin A.G. (Editors), Proceedings of 4th Workshop "Group Analysis of Differential Equations and Integrable Systems" (Protaras, Cyprus, October 26-30, 2008), University of Cyprus, Nicosia, 2009, 256 pp.
  6. 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 3 (2006), no. 2, 400 pp. You can download pdf (1.94 Mb).
  7. 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.
  8. 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 50 (2004), Parts 1-3, 1528 pp.
  9. 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 43 (2002), Parts 1-2, 784 pp.
  10. 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 39 (2001), 160 pp.
  11. Boyko V.M., Nikitin A.G. and Popovych R.O. (Editors), Group and Analytic Methods in Mathematical Physics, Proceedings of Institute of Mathematics, Kyiv 36 (2001), 324 pp. You can download pdf (1.63 Mb) or pdf-booklet (1.53 Mb).
  12. 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 34 (2001), 240 pp.
  13. Vasilenko O.F., Popovych G.V. and Vertsanova E.V., Handbook on solving problems of mathematical programming (Editor: Popovych R.O.), Kyiv, MAUP, 1999, 200 pp.
  14. 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 19 (1998), 280 pp. You can download pdf (1.35 Mb) or pdf-booklet (1.27 Mb).
  15. 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 17 (1997), 248 pp.


Selected invited seminar talks

  1. Inverse problems on conservation laws of differential equations,
    11 September 2015, Math and Stats Colloquium, Department of Mathematics and Statistics, University of Saskatchewan (Saskatoon, Canada)
  2. Local conservation laws of differential equations: algorithms and further development,
    24 April 2013, CRM Applied Mathematics Seminar, Department of Mathematics and Statistics, McGill University (Montréal, Canada)
  3. Point transformations in classes of differential equations,
    11 June 2013, Math and Stats Colloquium, Department of Mathematics and Statistics, University of Saskatchewan (Saskatoon, Canada)
  4. Invariant discretization schemes for the shallow-water equations,
    30 May 2012, SYMMHD mini-workshop, Faculty of Engineering, Katholieke Universiteit Leuven, Campus Kortrijk (29-30 May 2012, Kortrijk, Belgium)