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.
Bihlo A. and Popovych R.O., Physics-informed neural networks for the shallow-water equations on the sphere, arXiv:2104.00615, 20 pp.
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.
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.
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.
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.
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. Nauka18(A1) (2005), 451–456.
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.
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.
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.
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.
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. A36 (2003), no. 26, 7337–7360).
Popovych R. and Boyko V., Differential invariants of one-parameter group of local transformations: one independent variable, Nonlinear Oscilations5 (2002), no. 2, 218–223 (in Ukrainian).
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.
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]
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).
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]
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]
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).
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).
Popovych R. and Boyko V., Differential invariants of one-parameter group of local transformation and integration of Riccati equation, Vestnik Samarskogo gosudarstvennogo universiteta18 (2001), no. 4, 49–56 (in Russian). [pdf]
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.
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).
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]
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]
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.
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.
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).
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).
Popovych H.V. and Popovych R.O., Solutions of Euler equations which have linear vorticity, Vestnik PGTU, 1996, no. 2, 255–260 (in Russian).
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).
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).
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].
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.
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.
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].
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).
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].
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].
Popovych R.O., On general solutions and 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).
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).
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).
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).
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).
