Edit Profile (opens in new tab) Popovych, Roman O. Co-Author Distance Author ID: popovych.roman-o Published as: Popovych, Roman O.; Popovych, R. O.; Popovych, Roman; Popovych, R. more...less Homepage: https://www.imath.kiev.ua/~rop/ Documents Indexed: 123 Publications since 1995, including 17 Additional arXiv Preprints 10 Contributions as Editor Co-Authors: 42 Co-Authors with 121 Joint Publications 902 Co-Co-Authors all top 5 Co-Authors 10 single-authored 30 Boyko, Vyacheslav M. 23 Bihlo, Alexander 20 Sophocleous, Christodoulos 16 Vaneeva, Olena O. 15 Ivanova, Nataliya M. 8 Dos Santos Cardoso-Bihlo, Elsa Maria 8 Kunzinger, Michael 8 Nikitin, Anatoly Glebovich 7 Opanasenko, Stanislav 6 Patera, Jiří 5 Eshraghi, Homayoon 5 Pocheketa, Oleksandr A. 3 Damianou, Pantelis Andrea 3 Jegorchenko, I. A. 3 Koval, Serhii D. 3 Nesterenko, Maryna O. 3 Popovych, Dmytro R. 3 Sergyeyev, Artur 2 Bihlo, Alex 2 Johnpillai, Andrew Gratien 2 Kurujyibwami, Célestin 2 Leach, Peter Gavin Lawrence 2 Lokaziuk, Oleksandra V. 2 Lutfullin, Maxim W. 2 Sakhnovich, Alexander L. 2 Shapoval, Nataliya M. 2 Vinnichenko, Oleksandra O. 1 Abedini, Yousefali 1 Basarab-Horwath, Peter 1 Bovdi, Victor A. 1 Brecht, Rüdiger 1 Cherniha, Roman M. 1 Cheviakov, Alexei F. 1 Diene, Adama 1 Ehorchenko, I. A. 1 Kontogiorgis, Stavros 1 Korneva, I. P. 1 Maharaj, Sunil D. 1 Maltseva, Diana S. 1 Poltavets, Nataliia 1 Rajaee, Leila 1 Samoĭlenko, Anatoliĭ Mykhaĭlovych 1 Skuratovskii, Ruslan V. 1 Tsyfra, Ivan M. 1 Zhdanov, Renat Z. all top 5 Serials 12 Journal of Mathematical Analysis and Applications 12 Journal of Mathematical Physics 6 Journal of Physics A: Mathematical and Theoretical 5 Acta Applicandae Mathematicae 5 Physica D 4 Physics Letters. A 4 Applied Mathematics Letters 4 Journal of Physics A: Mathematical and General 4 Dopovidi Natsional’noï Akademiï Nauk Ukraïny. Matematyka, Pryrodoznavstvo, Tekhnichni Nauky 4 Communications in Nonlinear Science and Numerical Simulation 4 Zbirnyk Prats’ Instytutu Matematyky NAN Ukraïny 2 Journal of Engineering Mathematics 2 Ukraïns’kyĭ Matematychnyĭ Zhurnal 2 Linear Algebra and its Applications 1 International Journal of Theoretical Physics 1 Journal of Computational Physics 1 Journal of Geometry and Physics 1 Applied Mathematics and Computation 1 Journal of Algebra 1 Journal of Differential Equations 1 Studies in Applied Mathematics 1 Bulgarian Journal of Physics 1 European Journal of Applied Mathematics 1 SIAM Journal on Scientific Computing 1 Nonlinear Dynamics 1 Chaos 1 Journal of Nonlinear Mathematical Physics 1 Lobachevskii Journal of Mathematics 1 Physica Scripta 1 Algebra and Discrete Mathematics 1 Communications in Theoretical Physics 1 Analysis and Mathematical Physics 1 Carpathian Mathematical Publications 1 Journal of Integrable Systems all top 5 Fields 92 Partial differential equations (35-XX) 19 Nonassociative rings and algebras (17-XX) 19 Global analysis, analysis on manifolds (58-XX) 18 Dynamical systems and ergodic theory (37-XX) 18 Fluid mechanics (76-XX) 13 Ordinary differential equations (34-XX) 10 General and overarching topics; collections (00-XX) 10 Topological groups, Lie groups (22-XX) 9 Quantum theory (81-XX) 5 Geophysics (86-XX) 4 Mechanics of deformable solids (74-XX) 3 Group theory and generalizations (20-XX) 3 Numerical analysis (65-XX) 2 Number theory (11-XX) 2 Differential geometry (53-XX) 2 Mechanics of particles and systems (70-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Operator theory (47-XX) 1 Computer science (68-XX) 1 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 94 Publications have been cited 1,172 times in 458 Documents Cited by ▼ Year ▼ Realizations of real low-dimensional Lie algebras. Zbl 1040.17021 Popovych, Roman O.; Boyko, Vyacheslav M.; Nesterenko, Maryna O.; Lutfullin, Maxim W. 72 2003 New results on group classification of nonlinear diffusion-convection equations. Zbl 1067.35006 Popovych, Roman O.; Ivanova, Nataliya M. 71 2004 Admissible transformations and normalized classes of nonlinear Schrödinger equations. Zbl 1216.35146 Popovych, Roman O.; Kunzinger, Michael; Eshraghi, Homayoon 63 2010 Enhanced group analysis and exact solutions of variable coefficient semilinear diffusion equations with a power source. Zbl 1242.35023 Vaneeva, O. O.; Popovych, R. O.; Sophocleous, C. 48 2009 Enhanced group analysis and conservation laws of variable coefficient reaction-diffusion equations with power nonlinearities. Zbl 1160.35365 Vaneeva, O. O.; Johnpillai, A. G.; Popovych, R. O.; Sophocleous, C. 46 2007 Group analysis of variable coefficient diffusion-convection equations. I: Enhanced group classification. Zbl 1257.35018 Ivanova, N. M.; Popovych, R. O.; Sophocleous, C. 34 2010 Conservation laws and potential symmetries of linear parabolic equations. Zbl 1185.35009 Popovych, Roman O.; Kunzinger, Michael; Ivanova, Nataliya M. 32 2008 Contractions of low-dimensional Lie algebras. Zbl 1112.17007 Nesterenko, Maryna; Popovych, Roman 32 2006 A precise definition of reduction of partial differential equations. Zbl 0936.35012 Zhdanov, R. Z.; Tsyfra, I. M.; Popovych, R. O. 31 1999 Extended group analysis of variable coefficient reaction-diffusion equations with exponential nonlinearities. Zbl 1252.35025 Vaneeva, O. O.; Popovych, R. O.; Sophocleous, C. 31 2012 Group classification of nonlinear Schrödinger equations. Zbl 0993.58020 Nikitin, A. G.; Popovych, R. O. 30 2001 Hierarchy of conservation laws of diffusion-convection equations. Zbl 1067.37083 Popovych, Roman O.; Ivanova, Nataliya M. 30 2005 Complete group classification of a class of nonlinear wave equations. Zbl 1282.35020 Bihlo, Alexander; Dos Santos Cardoso-Bihlo, Elsa; Popovych, Roman O. 27 2012 More common errors in finding exact solutions of nonlinear differential equations. I. Zbl 1222.35009 Popovych, Roman O.; Vaneeva, Olena O. 26 2010 Enhanced preliminary group classification of a class of generalized diffusion equations. Zbl 1222.35012 Dos Santos Cardoso-Bihlo, Elsa; Bihlo, Alexander; Popovych, Roman O. 24 2011 Symmetry preserving parameterization schemes. Zbl 1277.58021 Popovych, Roman O.; Bihlo, Alexander 24 2012 Potential nonclassical symmetries and solutions of fast diffusion equation. Zbl 1197.35145 Popovych, Roman O.; Vaneeva, Olena O.; Ivanova, Nataliya M. 24 2007 Conservation laws and normal forms of evolution equations. Zbl 1237.35142 Popovych, Roman O.; Sergyeyev, Artur 21 2010 Group classification of \((1+1)\)-dimensional Schrödinger equations with potentials and power nonlinearities. Zbl 1071.35117 Popovych, Roman O.; Ivanova, Nataliya M.; Eshraghi, Homayoon 19 2004 Classification of admissible transformations of differential equations. Zbl 1150.35313 Popovych, R. O. 19 2006 Potential equivalence transformations for nonlinear diffusion-convection equations. Zbl 1126.35340 Popovych, Roman O.; Ivanova, Nataliya M. 18 2005 Computation of invariants of Lie algebras by means of moving frames. Zbl 1106.17040 Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman 17 2006 Group classification and exact solutions of variable-coefficient generalized Burgers equations with linear damping. Zbl 1335.35006 Pocheketa, Oleksandr A.; Popovych, Roman O.; Vaneeva, Olena O. 16 2014 Generalized conditional symmetries of evolution equations. Zbl 1211.35021 Kunzinger, Michael; Popovych, Roman O. 16 2011 Algebraic method for group classification of \((1+1)\)-dimensional linear Schrödinger equations. Zbl 1409.35179 Kurujyibwami, Célestin; Basarab-Horwath, Peter; Popovych, Roman O. 15 2018 Group analysis of general Burgers-Korteweg-de Vries equations. Zbl 1375.35457 Opanasenko, Stanislav; Bihlo, Alexander; Popovych, Roman O. 14 2017 Group classification of linear evolution equations. Zbl 1368.35013 Bihlo, Alexander; Popovych, Roman O. 14 2017 Singular reduction operators in two dimensions. Zbl 1152.35303 Kunzinger, Michael; Popovych, Roman O. 14 2008 Invariant discretization schemes for the shallow-water equations. Zbl 1263.76056 Bihlo, Alexander; Popovych, Roman O. 14 2012 Lie symmetries and exact solutions of the barotropic vorticity equation. Zbl 1272.86001 Bihlo, Alexander; Popovych, Roman O. 14 2009 Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity. Zbl 1430.35011 Opanasenko, Stanislav; Boyko, Vyacheslav; Popovych, Roman O. 13 2020 Reduction operators of linear second-order parabolic equations. Zbl 1145.35316 Popovych, Roman O. 13 2008 Local conservation laws of second-order evolution equations. Zbl 1146.37039 Popovych, Roman O.; Samoilenko, Anatoly M. 12 2008 Group analysis of nonlinear fin equations. Zbl 1160.35320 Vaneeva, O. O.; Johnpillai, A. G.; Popovych, R. O.; Sophocleous, C. 12 2008 Extended symmetry analysis of generalized Burgers equations. Zbl 1374.35121 Pocheketa, Oleksandr A.; Popovych, Roman O. 11 2017 Singular reduction modules of differential equations. Zbl 1368.35014 Boyko, Vaycheslav M.; Kunzinger, Michael; Popovych, Roman O. 11 2016 Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients. Zbl 1260.34064 Boyko, Vyacheslav M.; Popovych, Roman O.; Shapoval, Nataliya M. 11 2013 Potential conservation laws. Zbl 1152.81522 Kunzinger, Michael; Popovych, Roman O. 10 2008 Is a nonclassical symmetry a symmetry? Zbl 1227.35033 Kunzinger, Michael; Popovych, Roman O. 10 2009 Lie symmetries of two-dimensional shallow water equations with variable bottom topography. Zbl 1445.35279 Bihlo, Alexander; Poltavets, Nataliia; Popovych, Roman O. 10 2020 On Lie reduction of the Navier-Stokes equations. Zbl 0936.35127 Popovych, R. 8 1995 Point symmetry group of the barotropic vorticity equation. Zbl 1234.35014 Bihlo, Alexander; Popovych, Roman O. 8 2011 Multi-dimensional quasi-simple waves in weakly dissipative flows. Zbl 1133.76009 Rajaee, Leila; Eshraghi, Homayoon; Popovych, Roman O. 8 2008 Exact solutions of a remarkable fin equation. Zbl 1149.76047 Popovych, R. O.; Sophocleous, C.; Vaneeva, O. O. 8 2008 Generalization of the algebraic method of group classification with application to nonlinear wave and elliptic equations. Zbl 1453.35011 Vaneeva, Olena O.; Bihlo, Alexander; Popovych, Roman O. 8 2020 On a class of \(Q\)-conditional symmetries and solutions of evolution equations. Zbl 0913.35145 Popovych, R. O. 7 1998 Lie symmetries of \((1+1)\)-dimensional cubic Schrödinger equation with potential. Zbl 1100.35524 Popovych, R. O.; Ivanova, N. M.; Eshraghi, H. 7 2004 Enhanced symmetry analysis of two-dimensional Burgers system. Zbl 1423.35342 Kontogiorgis, Stavros; Popovych, Roman O.; Sophocleous, Christodoulos 7 2019 Invariants of Lie algebras with fixed structure of nilradicals. Zbl 1183.17003 Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman 6 2007 Complete point symmetry group of the barotropic vorticity equation on a rotating sphere. Zbl 1360.35009 Dos Santos Cardoso-Bihlo, Elsa; Popovych, Roman O. 6 2013 Equivalence of conservation laws and equivalence of potential systems. Zbl 1131.82032 Ivanova, N. M.; Popovych, R. O. 6 2007 Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements. Zbl 1168.17005 Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman 6 2008 Reduction operators and exact solutions of generalized Burgers equations. Zbl 1266.35125 Pocheketa, Oleksandr A.; Popovych, Roman O. 6 2012 A complete classification of the Lie symmetries for systems of nonlinear two-dimensional Laplace equations. Zbl 1003.35022 Popovych, R. O.; Cherniha, R. M. 5 2001 Invariant parameterization and turbulence modeling on the beta-plane. Zbl 1302.76078 Bihlo, Alexander; Dos Santos Cardoso-Bihlo, Elsa; Popovych, Roman O. 5 2014 Lie symmetry analysis and exact solutions of the quasigeostrophic two-layer problem. Zbl 1315.86001 Bihlo, Alexander; Popovych, Roman O. 5 2011 Reduction operators of variable coefficient semilinear diffusion equations with an exponential source. Zbl 1234.35022 Vaneeva, Olena; Popovych, Roman; Sophocleous, Christodoulos 5 2011 Physics-informed neural networks for the shallow-water equations on the sphere. Zbl 07518102 Bihlo, Alex; Popovych, Roman O. 5 2022 Inverse problem on conservation laws. Zbl 1453.35192 Popovych, Roman O.; Bihlo, Alexander 5 2020 Reduction operators of variable coefficient semilinear diffusion equations with a power source. Zbl 1223.35029 Vaneeva, O. O.; Popovych, R. O.; Sophocleous, C. 5 2009 Reduction operators of Burgers equation. Zbl 1252.35231 Pocheketa, Oleksandr A.; Popovych, Roman O. 5 2013 Equivalence groupoid and group classification of a class of variable-coefficient Burgers equations. Zbl 1447.35020 Opanasenko, Stanislav; Bihlo, Alexander; Popovych, Roman O. 5 2020 Symmetry analysis of barotropic potential vorticity equation. Zbl 1182.76937 Bihlo, Alexander; Popovych, Roman O. 4 2009 Variational symmetries and conservation laws of the wave equation in one space dimension. Zbl 1437.35012 Popovych, Roman O.; Cheviakov, Alexei F. 4 2020 Equivalence groupoids and group classification of multidimensional nonlinear Schrödinger equations. Zbl 1450.37061 Kurujyibwami, Célestin; Popovych, Roman O. 4 2020 On \(Q\)-conditional symmetry of the linear \(n\)-dimensional heat equation. Zbl 0912.35070 Popovych, R. O.; Korneva, I. P. 3 1998 Group classification of the Fisher equation with time-dependent coefficients. Zbl 1292.35018 Vaneeva, O. O.; Popovych, R. O.; Sophocleous, C. 3 2013 Equivalence of diagonal contractions to generalized IW-contractions with integer exponents. Zbl 1185.17005 Popovych, Dmytro R.; Popovych, Roman O. 3 2009 Lie reduction and exact solutions of vorticity equation on rotating sphere. Zbl 1255.86005 Bihlo, Alexander; Popovych, Roman O. 3 2012 Zeroth-order conservation laws of two-dimensional shallow water equations with variable bottom topography. Zbl 1454.76018 Bihlo, Alexander; Popovych, Roman O. 3 2020 Group classification of generalized eikonal equations. Zbl 1036.35013 Popovych, R. O.; Ehorchenko, I. A. 2 2001 Equivalence of \(Q\)-conditional symmetries under group of local transformation. Zbl 0953.35009 Popovych, Roman O. 2 2000 Extended symmetry analysis of two-dimensional degenerate Burgers equation. Zbl 1473.35019 Vaneeva, Olena O.; Popovych, Roman O.; Sophocleous, Christodoulos 2 2021 Mapping method of group classification. Zbl 1487.35023 Opanasenko, Stanislav; Popovych, Roman O. 2 2022 Extended symmetry analysis of an isothermal no-slip drift flux model. Zbl 1453.76186 Opanasenko, Stanislav; Bihlo, Alexander; Popovych, Roman O.; Sergyeyev, Artur 2 2020 Invariants of Lie algebras via moving frames. Zbl 1251.17006 Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman 2 2009 Lowest-dimensional example on non-universality of generalized Inönü-Wigner contractions. Zbl 1250.17005 Popovych, Dmytro R.; Popovych, Roman O. 2 2010 Symmetry justification of Lorenz’ maximum simplification. Zbl 1204.37026 Bihlo, Alexander; Popovych, Roman O. 2 2010 Differential invariants for a class of diffusion equations. Zbl 1438.35007 Dos Santos Cardoso-Bihlo, E.; Bihlo, A.; Popovych, R. O. 2 2019 Normalized classes of nonlinear Schrödinger equations. Zbl 1342.35352 Popovych, R. 2 2006 No-go theorem on reduction operators of linear second-order parabolic equations. Zbl 1150.35425 Popovych, R. O. 2 2006 Invariants of triangular Lie algebras. Zbl 1121.17008 Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman 2 2007 Invariants of triangular Lie algebras with one nil-independent diagonal element. Zbl 1185.17008 Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman 2 2007 Differential invariants and application to Riccati-type systems. Zbl 1044.53012 Popovych, Roman O.; Boyko, Vyacheslav M. 2 2002 Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein-Gordon equations. Zbl 1472.35019 Boyko, Vyacheslav M.; Lokaziuk, Oleksandra V.; Popovych, Roman O. 2 2021 Generalized symmetries and conservation laws of (1 + 1)-dimensional Klein-Gordon equation. Zbl 1454.81071 Opanasenko, Stanislav; Popovych, Roman O. 2 2020 On reduction and \(Q\)-conditional (nonclassical) symmetry. Zbl 0954.35040 Popovych, Roman 1 1997 Conditional symmetries of the linear rod equation. Zbl 1289.35319 Bojko, V. M.; Popovych, R. O. 1 2013 Reduction operators of the linear rod equation. Zbl 1292.35163 Boyko, Vyacheslav M.; Popovych, Roman O. 1 2013 Simplest potential conservation laws of linear evolution equations. Zbl 1234.35015 Boyko, Vyacheslav M.; Popovych, Roman O. 1 2011 Point and contact equivalence groupoids of two-dimensional quasilinear hyperbolic equations. Zbl 1462.35021 Popovych, Roman O. 1 2021 Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model. Zbl 1486.35014 Opanasenko, Stanislav; Bihlo, Alexander; Popovych, Roman O.; Sergyeyev, Artur 1 2020 Proceedings of the 6th international workshop on group analysis of differential equations and integrable systems, Protaras, Cyprus, June 17–21, 2012. Zbl 1264.35004 1 2013 Extended symmetry analysis of remarkable (1+2)-dimensional Fokker-Planck equation. Zbl 1522.35023 Koval, Serhii D.; Bihlo, Alexander; Popovych, Roman O. 1 2023 Extended symmetry analysis of remarkable (1+2)-dimensional Fokker-Planck equation. Zbl 1522.35023 Koval, Serhii D.; Bihlo, Alexander; Popovych, Roman O. 1 2023 Physics-informed neural networks for the shallow-water equations on the sphere. Zbl 07518102 Bihlo, Alex; Popovych, Roman O. 5 2022 Mapping method of group classification. Zbl 1487.35023 Opanasenko, Stanislav; Popovych, Roman O. 2 2022 Extended symmetry analysis of two-dimensional degenerate Burgers equation. Zbl 1473.35019 Vaneeva, Olena O.; Popovych, Roman O.; Sophocleous, Christodoulos 2 2021 Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein-Gordon equations. Zbl 1472.35019 Boyko, Vyacheslav M.; Lokaziuk, Oleksandra V.; Popovych, Roman O. 2 2021 Point and contact equivalence groupoids of two-dimensional quasilinear hyperbolic equations. Zbl 1462.35021 Popovych, Roman O. 1 2021 Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity. Zbl 1430.35011 Opanasenko, Stanislav; Boyko, Vyacheslav; Popovych, Roman O. 13 2020 Lie symmetries of two-dimensional shallow water equations with variable bottom topography. Zbl 1445.35279 Bihlo, Alexander; Poltavets, Nataliia; Popovych, Roman O. 10 2020 Generalization of the algebraic method of group classification with application to nonlinear wave and elliptic equations. Zbl 1453.35011 Vaneeva, Olena O.; Bihlo, Alexander; Popovych, Roman O. 8 2020 Inverse problem on conservation laws. Zbl 1453.35192 Popovych, Roman O.; Bihlo, Alexander 5 2020 Equivalence groupoid and group classification of a class of variable-coefficient Burgers equations. Zbl 1447.35020 Opanasenko, Stanislav; Bihlo, Alexander; Popovych, Roman O. 5 2020 Variational symmetries and conservation laws of the wave equation in one space dimension. Zbl 1437.35012 Popovych, Roman O.; Cheviakov, Alexei F. 4 2020 Equivalence groupoids and group classification of multidimensional nonlinear Schrödinger equations. Zbl 1450.37061 Kurujyibwami, Célestin; Popovych, Roman O. 4 2020 Zeroth-order conservation laws of two-dimensional shallow water equations with variable bottom topography. Zbl 1454.76018 Bihlo, Alexander; Popovych, Roman O. 3 2020 Extended symmetry analysis of an isothermal no-slip drift flux model. Zbl 1453.76186 Opanasenko, Stanislav; Bihlo, Alexander; Popovych, Roman O.; Sergyeyev, Artur 2 2020 Generalized symmetries and conservation laws of (1 + 1)-dimensional Klein-Gordon equation. Zbl 1454.81071 Opanasenko, Stanislav; Popovych, Roman O. 2 2020 Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model. Zbl 1486.35014 Opanasenko, Stanislav; Bihlo, Alexander; Popovych, Roman O.; Sergyeyev, Artur 1 2020 Enhanced symmetry analysis of two-dimensional Burgers system. Zbl 1423.35342 Kontogiorgis, Stavros; Popovych, Roman O.; Sophocleous, Christodoulos 7 2019 Differential invariants for a class of diffusion equations. Zbl 1438.35007 Dos Santos Cardoso-Bihlo, E.; Bihlo, A.; Popovych, R. O. 2 2019 Algebraic method for group classification of \((1+1)\)-dimensional linear Schrödinger equations. Zbl 1409.35179 Kurujyibwami, Célestin; Basarab-Horwath, Peter; Popovych, Roman O. 15 2018 Group analysis of general Burgers-Korteweg-de Vries equations. Zbl 1375.35457 Opanasenko, Stanislav; Bihlo, Alexander; Popovych, Roman O. 14 2017 Group classification of linear evolution equations. Zbl 1368.35013 Bihlo, Alexander; Popovych, Roman O. 14 2017 Extended symmetry analysis of generalized Burgers equations. Zbl 1374.35121 Pocheketa, Oleksandr A.; Popovych, Roman O. 11 2017 Singular reduction modules of differential equations. Zbl 1368.35014 Boyko, Vaycheslav M.; Kunzinger, Michael; Popovych, Roman O. 11 2016 Group classification and exact solutions of variable-coefficient generalized Burgers equations with linear damping. Zbl 1335.35006 Pocheketa, Oleksandr A.; Popovych, Roman O.; Vaneeva, Olena O. 16 2014 Invariant parameterization and turbulence modeling on the beta-plane. Zbl 1302.76078 Bihlo, Alexander; Dos Santos Cardoso-Bihlo, Elsa; Popovych, Roman O. 5 2014 Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients. Zbl 1260.34064 Boyko, Vyacheslav M.; Popovych, Roman O.; Shapoval, Nataliya M. 11 2013 Complete point symmetry group of the barotropic vorticity equation on a rotating sphere. Zbl 1360.35009 Dos Santos Cardoso-Bihlo, Elsa; Popovych, Roman O. 6 2013 Reduction operators of Burgers equation. Zbl 1252.35231 Pocheketa, Oleksandr A.; Popovych, Roman O. 5 2013 Group classification of the Fisher equation with time-dependent coefficients. Zbl 1292.35018 Vaneeva, O. O.; Popovych, R. O.; Sophocleous, C. 3 2013 Conditional symmetries of the linear rod equation. Zbl 1289.35319 Bojko, V. M.; Popovych, R. O. 1 2013 Reduction operators of the linear rod equation. Zbl 1292.35163 Boyko, Vyacheslav M.; Popovych, Roman O. 1 2013 Proceedings of the 6th international workshop on group analysis of differential equations and integrable systems, Protaras, Cyprus, June 17–21, 2012. Zbl 1264.35004 1 2013 Extended group analysis of variable coefficient reaction-diffusion equations with exponential nonlinearities. Zbl 1252.35025 Vaneeva, O. O.; Popovych, R. O.; Sophocleous, C. 31 2012 Complete group classification of a class of nonlinear wave equations. Zbl 1282.35020 Bihlo, Alexander; Dos Santos Cardoso-Bihlo, Elsa; Popovych, Roman O. 27 2012 Symmetry preserving parameterization schemes. Zbl 1277.58021 Popovych, Roman O.; Bihlo, Alexander 24 2012 Invariant discretization schemes for the shallow-water equations. Zbl 1263.76056 Bihlo, Alexander; Popovych, Roman O. 14 2012 Reduction operators and exact solutions of generalized Burgers equations. Zbl 1266.35125 Pocheketa, Oleksandr A.; Popovych, Roman O. 6 2012 Lie reduction and exact solutions of vorticity equation on rotating sphere. Zbl 1255.86005 Bihlo, Alexander; Popovych, Roman O. 3 2012 Enhanced preliminary group classification of a class of generalized diffusion equations. Zbl 1222.35012 Dos Santos Cardoso-Bihlo, Elsa; Bihlo, Alexander; Popovych, Roman O. 24 2011 Generalized conditional symmetries of evolution equations. Zbl 1211.35021 Kunzinger, Michael; Popovych, Roman O. 16 2011 Point symmetry group of the barotropic vorticity equation. Zbl 1234.35014 Bihlo, Alexander; Popovych, Roman O. 8 2011 Lie symmetry analysis and exact solutions of the quasigeostrophic two-layer problem. Zbl 1315.86001 Bihlo, Alexander; Popovych, Roman O. 5 2011 Reduction operators of variable coefficient semilinear diffusion equations with an exponential source. Zbl 1234.35022 Vaneeva, Olena; Popovych, Roman; Sophocleous, Christodoulos 5 2011 Simplest potential conservation laws of linear evolution equations. Zbl 1234.35015 Boyko, Vyacheslav M.; Popovych, Roman O. 1 2011 Admissible transformations and normalized classes of nonlinear Schrödinger equations. Zbl 1216.35146 Popovych, Roman O.; Kunzinger, Michael; Eshraghi, Homayoon 63 2010 Group analysis of variable coefficient diffusion-convection equations. I: Enhanced group classification. Zbl 1257.35018 Ivanova, N. M.; Popovych, R. O.; Sophocleous, C. 34 2010 More common errors in finding exact solutions of nonlinear differential equations. I. Zbl 1222.35009 Popovych, Roman O.; Vaneeva, Olena O. 26 2010 Conservation laws and normal forms of evolution equations. Zbl 1237.35142 Popovych, Roman O.; Sergyeyev, Artur 21 2010 Lowest-dimensional example on non-universality of generalized Inönü-Wigner contractions. Zbl 1250.17005 Popovych, Dmytro R.; Popovych, Roman O. 2 2010 Symmetry justification of Lorenz’ maximum simplification. Zbl 1204.37026 Bihlo, Alexander; Popovych, Roman O. 2 2010 Enhanced group analysis and exact solutions of variable coefficient semilinear diffusion equations with a power source. Zbl 1242.35023 Vaneeva, O. O.; Popovych, R. O.; Sophocleous, C. 48 2009 Lie symmetries and exact solutions of the barotropic vorticity equation. Zbl 1272.86001 Bihlo, Alexander; Popovych, Roman O. 14 2009 Is a nonclassical symmetry a symmetry? Zbl 1227.35033 Kunzinger, Michael; Popovych, Roman O. 10 2009 Reduction operators of variable coefficient semilinear diffusion equations with a power source. Zbl 1223.35029 Vaneeva, O. O.; Popovych, R. O.; Sophocleous, C. 5 2009 Symmetry analysis of barotropic potential vorticity equation. Zbl 1182.76937 Bihlo, Alexander; Popovych, Roman O. 4 2009 Equivalence of diagonal contractions to generalized IW-contractions with integer exponents. Zbl 1185.17005 Popovych, Dmytro R.; Popovych, Roman O. 3 2009 Invariants of Lie algebras via moving frames. Zbl 1251.17006 Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman 2 2009 Conservation laws and potential symmetries of linear parabolic equations. Zbl 1185.35009 Popovych, Roman O.; Kunzinger, Michael; Ivanova, Nataliya M. 32 2008 Singular reduction operators in two dimensions. Zbl 1152.35303 Kunzinger, Michael; Popovych, Roman O. 14 2008 Reduction operators of linear second-order parabolic equations. Zbl 1145.35316 Popovych, Roman O. 13 2008 Local conservation laws of second-order evolution equations. Zbl 1146.37039 Popovych, Roman O.; Samoilenko, Anatoly M. 12 2008 Group analysis of nonlinear fin equations. Zbl 1160.35320 Vaneeva, O. O.; Johnpillai, A. G.; Popovych, R. O.; Sophocleous, C. 12 2008 Potential conservation laws. Zbl 1152.81522 Kunzinger, Michael; Popovych, Roman O. 10 2008 Multi-dimensional quasi-simple waves in weakly dissipative flows. Zbl 1133.76009 Rajaee, Leila; Eshraghi, Homayoon; Popovych, Roman O. 8 2008 Exact solutions of a remarkable fin equation. Zbl 1149.76047 Popovych, R. O.; Sophocleous, C.; Vaneeva, O. O. 8 2008 Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements. Zbl 1168.17005 Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman 6 2008 Enhanced group analysis and conservation laws of variable coefficient reaction-diffusion equations with power nonlinearities. Zbl 1160.35365 Vaneeva, O. O.; Johnpillai, A. G.; Popovych, R. O.; Sophocleous, C. 46 2007 Potential nonclassical symmetries and solutions of fast diffusion equation. Zbl 1197.35145 Popovych, Roman O.; Vaneeva, Olena O.; Ivanova, Nataliya M. 24 2007 Invariants of Lie algebras with fixed structure of nilradicals. Zbl 1183.17003 Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman 6 2007 Equivalence of conservation laws and equivalence of potential systems. Zbl 1131.82032 Ivanova, N. M.; Popovych, R. O. 6 2007 Invariants of triangular Lie algebras. Zbl 1121.17008 Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman 2 2007 Invariants of triangular Lie algebras with one nil-independent diagonal element. Zbl 1185.17008 Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman 2 2007 Contractions of low-dimensional Lie algebras. Zbl 1112.17007 Nesterenko, Maryna; Popovych, Roman 32 2006 Classification of admissible transformations of differential equations. Zbl 1150.35313 Popovych, R. O. 19 2006 Computation of invariants of Lie algebras by means of moving frames. Zbl 1106.17040 Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman 17 2006 Normalized classes of nonlinear Schrödinger equations. Zbl 1342.35352 Popovych, R. 2 2006 No-go theorem on reduction operators of linear second-order parabolic equations. Zbl 1150.35425 Popovych, R. O. 2 2006 Hierarchy of conservation laws of diffusion-convection equations. Zbl 1067.37083 Popovych, Roman O.; Ivanova, Nataliya M. 30 2005 Potential equivalence transformations for nonlinear diffusion-convection equations. Zbl 1126.35340 Popovych, Roman O.; Ivanova, Nataliya M. 18 2005 New results on group classification of nonlinear diffusion-convection equations. Zbl 1067.35006 Popovych, Roman O.; Ivanova, Nataliya M. 71 2004 Group classification of \((1+1)\)-dimensional Schrödinger equations with potentials and power nonlinearities. Zbl 1071.35117 Popovych, Roman O.; Ivanova, Nataliya M.; Eshraghi, Homayoon 19 2004 Lie symmetries of \((1+1)\)-dimensional cubic Schrödinger equation with potential. Zbl 1100.35524 Popovych, R. O.; Ivanova, N. M.; Eshraghi, H. 7 2004 Realizations of real low-dimensional Lie algebras. Zbl 1040.17021 Popovych, Roman O.; Boyko, Vyacheslav M.; Nesterenko, Maryna O.; Lutfullin, Maxim W. 72 2003 Differential invariants and application to Riccati-type systems. Zbl 1044.53012 Popovych, Roman O.; Boyko, Vyacheslav M. 2 2002 Group classification of nonlinear Schrödinger equations. Zbl 0993.58020 Nikitin, A. G.; Popovych, R. O. 30 2001 A complete classification of the Lie symmetries for systems of nonlinear two-dimensional Laplace equations. Zbl 1003.35022 Popovych, R. O.; Cherniha, R. M. 5 2001 Group classification of generalized eikonal equations. Zbl 1036.35013 Popovych, R. O.; Ehorchenko, I. A. 2 2001 Equivalence of \(Q\)-conditional symmetries under group of local transformation. Zbl 0953.35009 Popovych, Roman O. 2 2000 A precise definition of reduction of partial differential equations. Zbl 0936.35012 Zhdanov, R. Z.; Tsyfra, I. M.; Popovych, R. O. 31 1999 On a class of \(Q\)-conditional symmetries and solutions of evolution equations. Zbl 0913.35145 Popovych, R. O. 7 1998 On \(Q\)-conditional symmetry of the linear \(n\)-dimensional heat equation. Zbl 0912.35070 Popovych, R. O.; Korneva, I. P. 3 1998 On reduction and \(Q\)-conditional (nonclassical) symmetry. Zbl 0954.35040 Popovych, Roman 1 1997 On Lie reduction of the Navier-Stokes equations. Zbl 0936.35127 Popovych, R. 8 1995 all cited Publications top 5 cited Publications all top 5 Cited by 505 Authors 55 Popovych, Roman O. 33 Sophocleous, Christodoulos 19 Bihlo, Alexander 19 Vaneeva, Olena O. 17 Ivanova, Nataliya M. 16 Meleshko, Sergey V. 11 Cheviakov, Alexei F. 10 Moitsheki, Raseelo J. 9 Bluman, George Wallace 9 Sergyeyev, Artur 8 Freire, Igor Leite 7 Boyko, Vyacheslav M. 7 Huang, Dingjiang 7 Nikitin, Anatoly Glebovich 7 Opanasenko, Stanislav 7 Serov, Mykola I. 7 Tracinà, Rita 6 Alvarez, María Alejandra 6 Ayub, Muhammad 6 Dorodnitsyn, Vladimir A. 6 Güngör, Faruk 6 Kunzinger, Michael 6 Leach, Peter Gavin Lawrence 6 Moyo, Sibusiso 6 Polyanin, Andrei Dmitrievich 6 Tsyfra, Ivan M. 5 Bruzón, Maria Santos 5 Campoamor-Stursberg, Rutwig 5 Christou, Marios Andreas 5 Dos Santos Cardoso-Bihlo, Elsa Maria 5 Gandarias Núñez, Maria Luz 5 Ji, Lina 5 Mahomed, Fazal M. 5 Paliathanasis, Andronikos 5 Rezaei-Aghdam, Adel 5 Zhang, Zhiyong 5 Zhdanov, Renat Z. 4 Anco, Stephen C. 4 Ceballos, Manuel 4 Cicogna, Giampaolo 4 Cimpoiasu, Rodica 4 Davydovych, Vasyl V. 4 Haghighatdoost, Ghorbanali 4 Huang, Qing 4 Kara, Abdul Hamid 4 Kontogiorgis, Stavros 4 Kudryashov, Nikolaĭ Alekseevich 4 Levi, Decio 4 Nadjafikhah, Mehdi 4 Rassokha, Inna V. 4 Thomova, Zora 4 Tsaousi, C. 3 Agore, Ana-Loredana 3 Basarab-Horwath, Peter 3 Biggs, Rory 3 Bihlo, Alex 3 Bozhkov, Yuri Dimitrov 3 Bradshaw-Hajek, Bronwyn H. 3 Chaolu, Temuer 3 Cherniha, Roman M. 3 Czyżycki, Tomasz 3 da Silva, Priscila Leal 3 Eshaghi Gordji, Madjid 3 Eshraghi, Homayoon 3 Fialowski, Alice 3 Gupta, Rajesh Kumar 3 Hernández, Isabel 3 Hrivnák, Jiří 3 Johnpillai, Andrew Gratien 3 Kalnins, Ernest G. 3 Kaygorodov, Ivan 3 Khan, Masood 3 Magda, Olena V. 3 Miller, Willard jun. 3 Mustafa, Muhammad Tahir 3 Naz, Rehana 3 Ndogmo, Jean-Claude 3 Nesterenko, Maryna O. 3 Oguis, G. F. 3 Olver, Peter John 3 Omirov, Bakhrom A. 3 Penkava, Michael 3 Pocheketa, Oleksandr A. 3 Popovych, Dmytro R. 3 Pošta, Severin 3 Remsing, Claudiu-Cristian 3 Rodríguez, Miguel Angel 3 Siriwat, Piyanuch 3 Towers, David A. 3 Tychynin, V. A. 3 Valiquette, Francis 3 Wang, Gangwei 3 Winternitz, Pavel 3 Yuryk, Ivan I. 3 Zhou, Shuigeng 3 Zhurov, Alexei I. 2 Ali, Ahmed M. S. 2 Ali, Sajid 2 Amirzadeh-Fard, H. 2 Azad, Hassan ...and 405 more Authors all top 5 Cited in 112 Serials 54 Journal of Mathematical Physics 46 Journal of Mathematical Analysis and Applications 37 Communications in Nonlinear Science and Numerical Simulation 19 Applied Mathematics and Computation 14 Applied Mathematics Letters 12 Mathematical Methods in the Applied Sciences 11 Acta Applicandae Mathematicae 11 Nonlinear Dynamics 11 Journal of Nonlinear Mathematical Physics 10 Journal of Geometry and Physics 10 Journal of Physics A: Mathematical and Theoretical 9 Linear Algebra and its Applications 8 Abstract and Applied Analysis 8 Nonlinear Analysis. Real World Applications 7 Ukrainian Mathematical Journal 7 Advances in Mathematical Physics 6 Journal of Engineering Mathematics 6 Physica D 5 Linear and Multilinear Algebra 5 Journal of Algebra 5 Symmetry 4 International Journal of Theoretical Physics 4 Journal of Computational Physics 4 Journal of Computational and Applied Mathematics 4 Studies in Applied Mathematics 4 European Journal of Applied Mathematics 4 Lobachevskii Journal of Mathematics 4 Journal of Applied Mathematics 4 International Journal of Geometric Methods in Modern Physics 4 Discrete and Continuous Dynamical Systems. Series S 3 Physics Letters. A 3 Journal of Differential Equations 3 Journal of Mathematical Sciences (New York) 3 Journal of High Energy Physics 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 International Journal of Applied and Computational Mathematics 2 Computers & Mathematics with Applications 2 Computer Methods in Applied Mechanics and Engineering 2 Reports on Mathematical Physics 2 Theoretical and Mathematical Physics 2 Reviews in Mathematical Physics 2 International Journal of Mathematics and Mathematical Sciences 2 Journal of Pure and Applied Algebra 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Quaestiones Mathematicae 2 Results in Mathematics 2 Journal of Symbolic Computation 2 Forum Mathematicum 2 Journal of Applied Mechanics and Technical Physics 2 International Journal of Nonlinear Sciences and Numerical Simulation 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Mediterranean Journal of Mathematics 2 Journal of Mathematical Physics, Analysis, Geometry 2 Analysis and Mathematical Physics 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Communications in Algebra 1 Computers and Fluids 1 Geophysical and Astrophysical Fluid Dynamics 1 Nuclear Physics. B 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Chaos, Solitons and Fractals 1 Journal of Optimization Theory and Applications 1 Mathematische Zeitschrift 1 Ricerche di Matematica 1 Annals of Global Analysis and Geometry 1 Bulletin of the Iranian Mathematical Society 1 Journal of Scientific Computing 1 Applied Mathematical Modelling 1 Continuum Mechanics and Thermodynamics 1 Applied Mathematics. Series B (English Edition) 1 Calculus of Variations and Partial Differential Equations 1 NoDEA. Nonlinear Differential Equations and Applications 1 Discrete and Continuous Dynamical Systems 1 Matematychni Metody ta Fizyko-Mekhanichni Polya 1 Doklady Mathematics 1 Mathematical Physics, Analysis and Geometry 1 Soft Computing 1 Algebras and Representation Theory 1 Chaos 1 Regular and Chaotic Dynamics 1 Journal of Dynamical and Control Systems 1 Communications in Contemporary Mathematics 1 Applied Sciences 1 Qualitative Theory of Dynamical Systems 1 Differential Equations 1 Mathematical Modelling and Analysis 1 Journal of Systems Science and Complexity 1 Journal of Algebra and its Applications 1 Analysis and Applications (Singapore) 1 Fixed Point Theory and Applications 1 Mathematical Biosciences and Engineering 1 Waves in Random and Complex Media 1 Proyecciones 1 Journal of Noncommutative Geometry 1 Chinese Journal of Physics (Taipei) 1 Asian-European Journal of Mathematics 1 International Journal of Biomathematics 1 Communications in Theoretical Physics 1 Advances in Differential Equations and Control Processes 1 International Journal of Nonlinear Analysis and Applications ...and 12 more Serials all top 5 Cited in 43 Fields 279 Partial differential equations (35-XX) 74 Nonassociative rings and algebras (17-XX) 71 Dynamical systems and ergodic theory (37-XX) 68 Fluid mechanics (76-XX) 46 Ordinary differential equations (34-XX) 45 Global analysis, analysis on manifolds (58-XX) 32 Topological groups, Lie groups (22-XX) 29 Quantum theory (81-XX) 19 Mechanics of particles and systems (70-XX) 17 Differential geometry (53-XX) 15 Numerical analysis (65-XX) 13 Computer science (68-XX) 10 Mechanics of deformable solids (74-XX) 9 Classical thermodynamics, heat transfer (80-XX) 9 Geophysics (86-XX) 8 Biology and other natural sciences (92-XX) 7 Associative rings and algebras (16-XX) 7 Relativity and gravitational theory (83-XX) 6 Difference and functional equations (39-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Functional analysis (46-XX) 4 Probability theory and stochastic processes (60-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Commutative algebra (13-XX) 3 Group theory and generalizations (20-XX) 3 Special functions (33-XX) 3 Operator theory (47-XX) 3 Manifolds and cell complexes (57-XX) 3 Optics, electromagnetic theory (78-XX) 3 Systems theory; control (93-XX) 2 Algebraic geometry (14-XX) 2 Astronomy and astrophysics (85-XX) 2 Operations research, mathematical programming (90-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Category theory; homological algebra (18-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral equations (45-XX) 1 Geometry (51-XX) 1 General topology (54-XX) Citations by Year