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    2024

    1. Admissible transformations and Lie symmetries of linear systems of second-order ordinary differential equations
      BOYKO, Vyacheslav M., Oleksandra V. LOKAZIUK and Roman POPOVYCH. Admissible transformations and Lie symmetries of linear systems of second-order ordinary differential equations. Journal of Mathematical Analysis and Applications. San Diego (USA): Academic Press Inc. Elsevier Science, 2024, vol. 539, No 2, p. "128543-1"-"128543-51", 51 pp. ISSN 0022-247X. Available from: https://dx.doi.org/10.1016/j.jmaa.2024.128543.
      Journal of Mathematical Analysis and Applications
      RIV/47813059:19610/24:A0000170 Article in a journal. English. United States of America.
      Boyko, Vyacheslav M. (804 Ukraine, guarantor) -- Lokaziuk, Oleksandra V. (804 Ukraine) -- Popovych, Roman (804 Ukraine, belonging to the institution)
      Keywords in English: Algebraic method of group classification; Equivalence algebra; Equivalence group; Equivalence groupoid; Group classification of differential equations; Lie symmetry; Linear systems of second-order ordinary differential equations
      International impact: yes
      Reviewed: yes
      Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 20/3/2025 17:12.
      More: https://is.slu.cz/publication/82962/en
    2. Extended symmetry analysis of (1+2)-dimensional fine Kolmogorov backward equation
      KOVAL, Serhii D. and Roman POPOVYCH. Extended symmetry analysis of (1+2)-dimensional fine Kolmogorov backward equation. Studies in Applied Mathematics. Hoboken (USA): John Wiley and Sons, Inc., 2024, vol. 153, No 1, p. "e12695-1"-"e12695-30", 30 pp. ISSN 0022-2526. Available from: https://dx.doi.org/10.1111/sapm.12695.
      Studies in Applied Mathematics
      RIV/47813059:19610/24:A0000168 Article in a journal. English. United States of America.
      Koval, Serhii D. (804 Ukraine, guarantor) -- Popovych, Roman (804 Ukraine, belonging to the institution)
      Keywords in English: (1+2)-dimensional ultraparabolic linear Kolmogorov backward equations; classification of subalgebras; exact solutions; generalized symmetry; Lie reductions; point-symmetry group
      International impact: yes
      Reviewed: yes
      Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 20/3/2025 17:12.
      More: https://is.slu.cz/publication/82921/en
    3. Lie reductions and exact solutions of dispersionless Nizhnik equation
      VINNICHENKO, Oleksandra O., Vyacheslav M. BOYKO and Roman POPOVYCH. Lie reductions and exact solutions of dispersionless Nizhnik equation. Analysis and Mathematical Physics. Basel, Switzerland: Springer Basel AG, 2024, vol. 14, No 4, p. "82-1"-"82-56", 56 pp. ISSN 1664-2368. Available from: https://dx.doi.org/10.1007/s13324-024-00925-y.
      Analysis and Mathematical Physics
      RIV/47813059:19610/24:A0000169 Article in a journal. English. Switzerland.
      Vinnichenko, Oleksandra O. (804 Ukraine) -- Boyko, Vyacheslav M. (804 Ukraine, guarantor) -- Popovych, Roman (804 Ukraine, belonging to the institution)
      Keywords in English: dispersionless Nizhnik equation; Lie reduction; invariant solutions; point-symmetry pseudogroup; Lie invariance algebra; discrete symmetry; hidden symmetries
      International impact: yes
      Reviewed: yes
      Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 20/3/2025 17:13.
      More: https://is.slu.cz/publication/82923/en
    4. Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation
      BOYKO, Vyacheslav M., Roman POPOVYCH and Oleksandra O. VINNICHENKO. Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation. Communications in Nonlinear Science and Numerical Simulation. Amsterdam: Elsevier B.V., 2024, vol. 132, May, p. "107915-1"-"107915-19", 19 pp. ISSN 1007-5704. Available from: https://dx.doi.org/10.1016/j.cnsns.2024.107915.
      Communications in Nonlinear Science and Numerical Simulation
      RIV/47813059:19610/24:A0000166 Article in a journal. English. Netherlands.
      Boyko, Vyacheslav M. (804 Ukraine, guarantor) -- Popovych, Roman (804 Ukraine, belonging to the institution) -- Vinnichenko, Oleksandra O. (804 Ukraine)
      Keywords in English: Dispersionless Nizhnik equation; Point-symmetry pseudogroup; Lie invariance algebra; Discrete symmetry
      International impact: yes
      Reviewed: yes
      Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 20/3/2025 17:13.
      More: https://is.slu.cz/publication/82914/en
    5. Point-symmetry pseudogroup, Lie reductions and exact solutions of Boiti-Leon-Pempinelli system
      MALTSEVA, Diana S. and Roman POPOVYCH. Point-symmetry pseudogroup, Lie reductions and exact solutions of Boiti-Leon-Pempinelli system. Physica D: Nonlinear Phenomena. Amsterdam: Elsevier B.V., 2024, vol. 460, April, p. "134081-1"-"134081-21", 21 pp. ISSN 0167-2789. Available from: https://dx.doi.org/10.1016/j.physd.2024.134081.
      Physica D: Nonlinear Phenomena
      RIV/47813059:19610/24:A0000167 Article in a journal. English. Netherlands.
      Maltseva, Diana S. (804 Ukraine) -- Popovych, Roman (804 Ukraine, guarantor, belonging to the institution)
      Keywords in English: Boiti–Leon–Pempinelli system; Point-symmetry (pseudo)group; Lie reductions; Darboux transformation; Laplace transformation; Exact solutions
      International impact: yes
      Reviewed: yes
      Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 20/3/2025 17:13.
      More: https://is.slu.cz/publication/82920/en

    2023

    1. Extended symmetry analysis of remarkable (1+2)-dimensional Fokker-Planck equation
      KOVAL, Serhii D, Alexander BIHLO and Roman POPOVYCH. Extended symmetry analysis of remarkable (1+2)-dimensional Fokker-Planck equation. European Journal of Applied Mathematics. New York (USA): Cambridge University Press, 2023, vol. 34, No 5, p. 1067-1098. ISSN 0956-7925. Available from: https://dx.doi.org/10.1017/S0956792523000074.
      European Journal of Applied Mathematics
      RIV/47813059:19610/23:A0000141 Article in a journal. English. United States of America.
      Bihlo, Alexander (40 Austria) -- Popovych, Roman (804 Ukraine, guarantor, belonging to the institution)
      Keywords in English: (1+2)-dimensional ultraparabolic Fokker-Planck equation; complete point-symmetry pseudogroup; Lie symmetry; Lie reductions; exact solutions; Kramers equations
      International impact: yes
      Reviewed: yes
      Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 27/3/2024 14:38.
      More: https://is.slu.cz/publication/78264/en
    2. Point and generalized symmetries of the heat equation revisited
      KOVAL, Serhii D and Roman POPOVYCH. Point and generalized symmetries of the heat equation revisited. Journal of Mathematical Analysis and Applications. San Diego (USA): Academic Press Inc. Elsevier Science, 2023, vol. 527, No 2, p. "127430-1"-"127430-21", 21 pp. ISSN 0022-247X. Available from: https://dx.doi.org/10.1016/j.jmaa.2023.127430.
      Journal of Mathematical Analysis and Applications
      RIV/47813059:19610/23:A0000142 Article in a journal. English. United States of America.
      Popovych, Roman (804 Ukraine, guarantor, belonging to the institution)
      Keywords in English: Discrete symmetry; Generalized symmetry; Heat equation; Lie symmetry; Point-symmetry pseudogroup; Subalgebra classification
      International impact: yes
      Reviewed: yes
      Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 8/4/2024 13:06.
      More: https://is.slu.cz/publication/78283/en

    2022

    1. Mapping method of group classification
      OPANASENKO, Stanislav and Roman POPOVYCH. Mapping method of group classification. Journal of Mathematical Analysis and Applications. San Diego (USA): Academic Press Inc. Elsevier Science, 2022, vol. 513, No 2, p. "126209-1"-"126209-43", 43 pp. ISSN 0022-247X. Available from: https://dx.doi.org/10.1016/j.jmaa.2022.126209.
      Journal of Mathematical Analysis and Applications
      RIV/47813059:19610/22:A0000118 Article in a journal. English. United States of America.
      Opanasenko, Stanislav (804 Ukraine, guarantor) -- Popovych, Roman (804 Ukraine, belonging to the institution)
      Keywords in English: Lie symmetries; Group classification; Mapping method; Weakly similar classes; Fokker-Planck equations; Kolmogorov equations
      International impact: yes
      Reviewed: yes
      Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 9/3/2023 15:42.
      More: https://is.slu.cz/publication/65305/en

    2021

    1. Parameter-dependent linear ordinary differential equations and topology of domains
      POPOVYCH, Roman, Vyacheslav M. BOYKO and Michael KUNZINGER. Parameter-dependent linear ordinary differential equations and topology of domains. Journal of Differential Equations. San DIego (USA): Academic Press Inc. Elsevier Science, 2021, vol. 284, may, p. 546-575. ISSN 0022-0396. Available from: https://dx.doi.org/10.1016/j.jde.2021.03.001.
      Journal of Differential Equations
      RIV/47813059:19610/21:A0000105 Article in a journal. English. United States of America.
      Popovych, Roman (804 Ukraine, belonging to the institution) -- Boyko, Vyacheslav M. (804 Ukraine) -- Kunzinger, Michael (40 Austria, guarantor)
      Keywords in English: Parameter-dependent linear ODE; Fundamental set of solutions; Wronskian; Distributional solutions
      International impact: yes
      Reviewed: yes
      Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 29/4/2022 12:55.
      More: https://is.slu.cz/publication/60861/en

    2020

    1. Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity
      POPOVYCH, Roman, Stanislav OPANASENKO and Vyacheslav BOYKO. Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity. Journal of Mathematical Analysis and Applications. San Diego (USA): Academic Press Inc. Elsevier Science, 2020, vol. 484, No 1, p. "123739-1"-"123739-30", 30 pp. ISSN 0022-247X. Available from: https://dx.doi.org/10.1016/j.jmaa.2019.123739.
      Journal of Mathematical Analysis and Applications
      RIV/47813059:19610/20:A0000072 Article in a journal. English. United States of America.
      Popovych, Roman (804 Ukraine, belonging to the institution) -- Opanasenko, Stanislav (804 Ukraine, guarantor) -- Boyko, Vyacheslav (804 Ukraine)
      Keywords in English: Group classification of differential equations; Method of furcate splitting; Diffusion-reaction equations; Lie symmetry; Equivalence group; Lie reduction
      International impact: yes
      Reviewed: yes
      Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 6/4/2021 07:01.
      More: https://is.slu.cz/publication/39681/en
    2. Extended symmetry analysis of an isothermal no-slip drift flux model
      SERGYEYEV, Artur, Stanislav OPANASENKO, Alexander BIHLO and Roman POPOVYCH. Extended symmetry analysis of an isothermal no-slip drift flux model. Physica D: Nonlinear Phenomena. Amsterdam: Elsevier B.V., 2020, vol. 402, No 132188, p. "132188-1"-"132188-16", 16 pp. ISSN 0167-2789. Available from: https://dx.doi.org/10.1016/j.physd.2019.132188.
      Physica D: Nonlinear Phenomena
      RIV/47813059:19610/20:A0000064 Article in a journal. English. Netherlands.
      Sergyeyev, Artur (804 Ukraine, belonging to the institution) -- Opanasenko, Stanislav (804 Ukraine, guarantor) -- Bihlo, Alexander (40 Austria) -- Popovych, Roman (804 Ukraine, belonging to the institution)
      Keywords in English: Hydrodynamic-type system; Isothermal no-slip drift flux; Point symmetry; Exact solution; Generalized symmetry; Conservation law
      International impact: yes
      Reviewed: yes
      Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 6/4/2021 14:09.
      More: https://is.slu.cz/publication/39680/en
    3. Generalized symmetries and conservation laws of (1+1)-dimensional Klein-Gordon equation
      OPANASENKO, Stanislav and Roman POPOVYCH. Generalized symmetries and conservation laws of (1+1)-dimensional Klein-Gordon equation. Journal of Mathematical Physics. Melville (USA): American Institute of Physics, 2020, vol. 61, No 101515, p. "101515-1"-"101515-13", 13 pp. ISSN 0022-2488. Available from: https://dx.doi.org/10.1063/5.0003304.
      Journal of Mathematical Physics
      RIV/47813059:19610/20:A0000080 Article in a journal. English. United States of America.
      Opanasenko, Stanislav (804 Ukraine) -- Popovych, Roman (804 Ukraine, belonging to the institution)
      Keywords in English: Korteweg-De Vries equation; Classification; Operators; Systems; Fields; Euler
      International impact: yes
      Reviewed: yes
      Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 6/4/2021 13:39.
      More: https://is.slu.cz/publication/49266/en
    4. Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model
      OPANASENKO, Stanislav, Alexander BIHLO, Roman POPOVYCH and Artur SERGYEYEV. Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model. Physica D: Nonlinear Phenomena. Amsterdam: Elsevier B.V., 2020, vol. 411, No 132546, p. "132546-1"-"132546-19", 19 pp. ISSN 0167-2789. Available from: https://dx.doi.org/10.1016/j.physd.2020.132546.
      Physica D: Nonlinear Phenomena
      RIV/47813059:19610/20:A0000068 Article in a journal. English. Netherlands.
      Opanasenko, Stanislav (804 Ukraine, guarantor) -- Bihlo, Alexander (40 Austria) -- Popovych, Roman (804 Ukraine, belonging to the institution) -- Sergyeyev, Artur (804 Ukraine, belonging to the institution)
      Keywords in English: Generalized symmetry; Local conservation law; Recursion operator; Hamiltonian structure; Hydrodynamic-type system; Isothermal no-slip drift flux
      Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 6/4/2021 13:40.
      More: https://is.slu.cz/publication/49264/en

    2019

    1. Symmetries and conservation laws of differential equations
      POPOVYCH, Roman. Symmetries and conservation laws of differential equations. 2019.
      Name (in English): Symmetries and conservation laws of differential equations
      English.
      Keywords in English: Generalized conditional symmetry; Conditional Lie–Bäcklund symmetry; Evolution equation; Exact solution; Formal compatibility; Passive system; Energy conservation; Atmospheric dynamics; Lie algebras; Differential geometry; Algebraic methods; Partial differential equations; Invariance properties; Equations of fluid dynamics; Eddies; Vortex dynamics; Partial-Differential Equations; Direct Construction Method; Nonlocal Symmetries; Backlund-Transformations; Maxwells Equations; Partial-Differential-Equations; Heat-Equation; Nonclassical Symmetries; Diffusion Equation; Lie; Symmetry Reductions
      Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 16/4/2024 09:03.
      More: https://is.slu.cz/publication/78603/en

    2017

    1. Group analysis of general Burgers-Korteweg-de Vries equations
      OPANASENKO, Stanislav, Alexander BIHLO and Roman POPOVYCH. Group analysis of general Burgers-Korteweg-de Vries equations. Journal of Mathematical Physics. USA: American Institute of Physics, 2017, vol. 58, No 8, p. „081511-1“-„081511-37“, 37 pp. ISSN 0022-2488. Available from: https://dx.doi.org/10.1063/1.4997574.
      Journal of Mathematical Physics
      RIV/47813059:19610/17:A0000017 Article in a journal. English. United States of America.
      Opanasenko, Stanislav (804 Ukraine) -- Bihlo, Alexander (40 Austria) -- Popovych, Roman (804 Ukraine, guarantor, belonging to the institution)
      Keywords in English: Burgers-KdV equation; Group classification; Lie reduction
      International impact: yes
      Reviewed: yes
      Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 4/4/2018 13:30.
      More: https://is.slu.cz/publication/29848/en
Displayed: 4/4/2025 18:36