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Попович Роман Омелянович

Попович Роман Омелянович



Публікації

    ORCID: 0000-0003-2403-1525
    WoS ResearcherID:    I-8056-2012
    MR Author ID: 312897
    zbMATH Author ID: popovych.roman-o
    Scopus Author ID: 13406922000
    Google Scholar ID: 0dSY5OsAAAAJ

    1. Koval S.D. and Popovych R.O., Point and generalized symmetries of the heat equation revisited, J. Math. Anal. Appl. 527 (2023), 127430, 21 pp., arXiv:2208.11073.

    2. Koval S.D., Bihlo A. and Popovych R.O., Extended symmetry analysis of remarkable (1+2)-dimensional Fokker-Planck equation, European J. Appl. Math. 34 (2023), 1067–1098, arXiv:2205.13526.

    3. Opanasenko S. and Popovych R.O., Mapping method of group classification, J. Math. Anal. Appl. 513 (2022), 126209, 43 pp., arXiv:2109.11490.

    4. Bihlo A. and Popovych R.O., Physics-informed neural networks for the shallow-water equations on the sphere, J. Comp. Phys. 456 (2022), 111024, 18 pp., arXiv:2104.00615.

    5. Vaneeva O.O., Popovych R.O. and Sophocleous C., Enhanced symmetry analysis of two-dimensional degenerate Burgers equation, J. Geom. Phys. 169 (2021), 104336, 21 pp., arXiv:1908.01877.

    6. Dos Santos Cardoso-Bihlo E. and Popovych R.O., On the ineffectiveness of constant rotation in the primitive equations and their symmetry analysis, accepted to Commun. Nonlinear Sci. Numer. Simul. (2021), arXiv:1503.04168, 15 pp.

    7. Boyko V.M., Kunzinger M. and Popovych R.O., Parameter-dependent linear ordinary differential equations and topology of domains, J. Differential Equations, 284 (2021), 546–575, arXiv:1901.02059.

    8. Popovych R.O., Point and contact equivalence groupoids of two-dimensional quasilinear hyperbolic equations, Appl. Math. Lett. 116 (2021), 107068, 8 pp., arXiv:2009.07383.

    9. Boyko V.M., Lokaziuk O.V. and Popovych R.O., Admissible transformations and Lie symmetries of linear systems of second-order ordinary differential equations, arXiv:2105.05139, 49 pp.

    10. Bihlo A. and Popovych R.O., Physics-informed neural networks for the shallow-water equations on the sphere, arXiv:2104.00615, 20 pp.

    11. Maltseva D.S. and Popovych R.O., Complete point-symmetry group, Lie reductions and exact solutions of Boiti-Leon-Pempinelli system, arXiv:2103.08734, 36 pp.

    12. Opanasenko S. and Popovych R.O., Generalized symmetries and conservation laws of (1+1)-dimensional Klein–Gordon equation, J. Math. Phys. 61 (2020), 101515, 13 pp., arXiv:1810.12434.

    13. Bihlo A. and Popovych R.O., Zeroth-order conservation laws of two-dimensional shallow water equations with variable bottom topography, Stud. Appl. Math. 145 (2020), 291–321, arXiv:1912.11468.

    14. Bihlo A., Poltavets N. and Popovych R.O., Lie symmetries of two-dimensional shallow water equations with variable bottom topography, Chaos 30 (2020), 073132, 17 pp., arXiv:1911.02097.

    15. Popovych R.O. and Sakhnovich A., GBDT and explicit solutions for the matrix coupled dispersionless equations (local and nonlocal cases), J. Integrable Syst. 5 (2020), xyaa004, 24 pp., arXiv:1907.08258.

    16. Vaneeva O.O., Bihlo A. and Popovych R.O., Generalization of the algebraic method of group classification with application to nonlinear wave and elliptic equations, Commun. Nonlinear Sci. Numer. Simul. 91 (2020), 105419, 28 pp., arXiv:2002.08939.

    17. Kurujyibwami C. and Popovych R.O., Equivalence groupoids and group classification of multidimensional nonlinear Schrödinger equations, J. Math. Anal. Appl. 491 (2020), 124271, 35 pp., arXiv:2003.02781.

    18. Opanasenko S., Bihlo A., Popovych R.O. and Sergyeyev A., Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model, Phys. D 411 (2020), 132546, 19 pp., arXiv:1908.00034.

    19. Opanasenko S., Bihlo A. and Popovych R.O., Equivalence groupoid and group classification of a class of variable-coefficient Burgers equations, J. Math. Anal. Appl. 490 (2020), 124215, 22 pp., arXiv:1910.13500.

    20. Popovych R.O. and Cheviakov A.F., Variational symmetries and conservation laws of the wave equation in one space dimension, Appl. Math. Lett. 104 (2020), 106225, 7 pp., arXiv:1912.03698.

    21. Opanasenko S., Boyko V. and Popovych R.O., Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusion, J. Math. Anal. Appl. 484 (2020), 123739, 30 pp., arXiv:1804.08776.

    22. Opanasenko S., Bihlo A., Popovych R.O. and Sergyeyev A., Extended symmetry analysis of isothermal no-slip drift flux model, Phys. D 402 (2020), 132188, 16 pp., arXiv:1705.09277.

    23. Popovych R.O. and Bihlo A., Inverse problem on conservation laws, Phys. D 401 (2020), 132175, 16 pp., arXiv:1705.03547.

    24. Boyko V.M., Lokaziuk O.V. and Popovych R.O., Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein–Gordon equations, arXiv:2008.05460, 30 pp.

    25. Kontogiorgis S., Popovych R.O. and Sophocleous C., Enhanced symmetry analysis of two-dimensional Burgers system, Acta Appl. Math. 163 (2019), 91–128, arXiv:1709.02708.

    26. Dos Santos Cardoso-Bihlo E., Bihlo A. and Popovych R.O., Differential invariants for a class of diffusion equations, Symmetry and Integrability of Equations of Mathematical Physics, Collection of Works of Institute of Mathematics, Kyiv, 16 (2019), no. 1, 50–65, arXiv:1909.00477.

    27. Bihlo A., Dos Santos Cardoso-Bihlo E. and Popovych R.O., Invariant parameterization of geostrophic eddies in the ocean, arXiv:1908.06345, 21 pp.

    28. Vaneeva O.O., Popovych R.O. and Sophocleous C., Enhanced symmetry analysis of two-dimensional degenerate Burgers equation, arXiv:1908.01877, 26 pp.

    29. Kurujyibwami C., Basarab-Horwath P. and Popovych R.O., Algebraic method for group classification of (1+1)-dimensional linear Schrödinger equations, Acta Appl. Math. 157 (2018), 171–203, arXiv:1607.04118.

    30. Pocheketa O.A. and Popovych R.O., Extended symmetry analysis of generalized Burgers equations, J. Math. Phys. 58 (2017), 101501, 28 pp., arXiv:1603.09377.

    31. Opanasenko S., Bihlo A. and Popovych R.O., Group analysis of general Burgers–Korteweg–de Vries equations, J. Math. Phys. 58 (2017), 081511, 37 pp., arXiv:1703.06932.

    32. Bihlo A. and Popovych R.O., Group classification of linear evolution equations, J. Math. Anal. Appl. 448 (2017), 982–1005, arXiv:1605.09251.

    33. Boyko V.M., Kunzinger M. and Popovych R.O., Singular reduction modules of differential equations, J. Math. Phys. 57 (2016), 101503, 34 pp., arXiv:1201.3223.

    34. 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, Imperial College Press, London, 2015, pp. 483–524.

    35. Bihlo A., Dos Santos Cardoso-Bihlo E. and Popovych R.O., Algebraic method for finding equivalence groups, J. Phys.: Conf. Ser. 621 (2015) 012001, 17 pp., arXiv:1503.06487.

    36. 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.

    37. 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.

    38. 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.

    39. 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.

    40. 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.

    41. 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.

    42. Pocheketa O.A. and Popovych R.O., Reduction operators of Burgers equation, J. Math. Anal. Appl. 398 (2013), 270–277, arXiv:1208.0232.

    43. 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.

    44. 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.

    45. 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.

    46. 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.

    47. 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.

    48. 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.

    49. Popovych R.O. and Bihlo A., Symmetry preserving parameterization schemes, J. Math. Phys. 53 (2012), 073102, 36 pp., arXiv:1010.3010.

    50. 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.

    51. 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.

    52. Kunzinger M. and Popovych R.O., Generalized conditional symmetries of evolution equations, J. Math. Anal. Appl. 379 (2011), 444–460, arXiv:1011.0277.

    53. 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.

    54. 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.

    55. 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), University of Cyprus, Nicosia, 2011, 207–219, arXiv:1010.2046.

    56. 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), University of Cyprus, Nicosia, 2011, 15–27, arXiv:1009.1523.

    57. 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), University of Cyprus, Nicosia, 2011, 28–39, arXiv:1008.4851.

    58. 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.
    59. Popovych R.O. and Sergyeyev A., Conservation laws and normal forms of evolution equations, Phys. Lett. A 374 (2010), 2210–2217, arXiv:1003.1648.

    60. 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.

    61. 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.

    62. 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.

    63. Bihlo A. and Popovych R.O., Symmetry justification of Lorenz' maximum simplification, Nonlinear Dynam. 61 (2010), 101–107, arXiv:0805.4061.

    64. 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.

    65. 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.
    66. Bihlo A. and Popovych R.O., Symmetry analysis of barotropic potential vorticity equation, Commun. Theor. Phys. 52 (2009), 697–700, arXiv:0811.3008.

    67. 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.

    68. Ivanova N.M., Popovych R.O., Sophocleous C. and Vaneeva O.O., Conservation laws and hierarchies of potential symmetries for certain diffusion equations, Physica A 388 (2009), 343–356, arXiv:0806.1698.

    69. 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), University of Cyprus, Nicosia, 2009, 36–44, arXiv:0904.4462.

    70. 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), University of Cyprus, Nicosia, 2009, 191–209, arXiv:0904.3424.

    71. 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), University of Cyprus, Nicosia, 2009, 107–120, arXiv:0903.0821.

    72. Kunzinger M. and Popovych R.O., Singular reduction operators in two dimensions, J. Phys. A 41 (2008), 505201, 24 pp., arXiv:0808.3577.

    73. Kunzinger M. and Popovych R.O., Potential conservation laws, J. Math. Phys. 49 (2008), 103506, 34 pp., arXiv:0803.1156.

    74. 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.

    75. Popovych R.O., Reduction operators of linear second-order parabolic equations, J. Phys. A 41 (2008), 185202, 31 pp., arXiv:0712.2764.

    76. Rajaee L., Eshraghi H. and Popovych R.O., Multi-dimensional quasi-simple waves in weakly dissipative flows, Physica D 237 (2008), 405–419.

    77. 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.

    78. 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.

    79. 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.

    80. 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.

    81. 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.

    82. Boyko V.M., Patera J. and Popovych R.O., Invariants of triangular Lie algebras, J. Phys. A 40 (2007), 7557–7572, arXiv:0704.0937.

    83. 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.

    84. 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.

    85. 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.

    86. 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.

    87. Nesterenko M. and Popovych R.O., Contractions of low-dimensional Lie algebras, J. Math. Phys. 47 (2006), 123515, 45 pp., arXiv:math-ph/0608018.

    88. Popovych R.O., Direct methods of construction of conservation laws, Physics AUC 16(II) (2006), 81–94.

    89. Popovych R.O., Classification of admissible transformations of differential equations, Collection of Works of Institute of Mathematics, Kyiv, 3 (2006), no. 2, 239–254.

    90. 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.

    91. 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.

    92. 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.

    93. 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.

    94. 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.

    95. Eshraghi H., Abedini Y. and Popovych R.O., Effect of external sources on finite time singularity, Physica Scripta 71 (2005), 52–59.

    96. 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.

    97. 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), University of Cyprus, Nicosia, 2005, 107–113, arXiv:math-ph/0505015.

    98. 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), University of Cyprus, Nicosia, 2005, 167–174.

    99. 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.

    100. 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.

    101. 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.

    102. 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.

    103. 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.

    104. 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).

    105. 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).

    106. 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.

    107. 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]

    108. 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).

    109. 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]

    110. 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]

    111. 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).

    112. 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.

    113. Popovych R.O. and Yehorchenko I.A., Group classification of generalized eikonal equations, Ukr. Math. J. 53 (2001), no. 11, 1513–1520.

    114. 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).

    115. 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]

    116. 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.

    117. 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]

    118. 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.

    119. 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).

    120. 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]

    121. 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]

    122. 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.

    123. 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.

    124. 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).

    125. 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).

    126. 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.

    127. Popovych H.V. and Popovych R.O., Solutions of Euler equations which have linear vorticity, Vestnik PGTU, 1996, no. 2, 255–260 (in Russian).

    128. 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).

    129. Popovych R.O., On Lie reduction of the Navier–Stokes equations, J. Nonlinear Math. Phys. 2 (1995), no. 3–4, 301–311 [pdf].

    130. 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.

    131. 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).

    132. 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].

    133. 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].

    134. 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].

    135. 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.

    136. 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.

    137. 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].

    138. 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).

    139. 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].

    140. 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].

    141. Popovych R.O., On general solutions and symmetry of Navier–Stokes equations with additional condition  (→u⋅∇)→u=→0, Proceedings of the International conference dedicated the memory of acad. M.P. Kravchuk (Kyiv: Acad. Sci. Ukraine, Inst. Math.), 1992, 163 (in Ukrainian).

    142. 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).

    143. 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).

    144. 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).

    145. 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).
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