Boyko, Vyacheslav M.; Popovych, Roman O.; Vinnichenko, Oleksandra O. Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation. (English) Zbl 07822390 Commun. Nonlinear Sci. Numer. Simul. 132, Article ID 107915, 19 p. (2024). MSC: 35Axx 35Qxx 37Kxx PDFBibTeX XMLCite \textit{V. M. Boyko} et al., Commun. Nonlinear Sci. Numer. Simul. 132, Article ID 107915, 19 p. (2024; Zbl 07822390) Full Text: DOI arXiv
Vinnichenko, Oleksandra O.; Boyko, Vyacheslav M.; Popovych, Roman O. Lie reductions and exact solutions of dispersionless Nizhnik equation. arXiv:2308.03744 Preprint, arXiv:2308.03744 [math-ph] (2023). MSC: 35B06 17B80 35C05 35C06 35A30 BibTeX Cite \textit{O. O. Vinnichenko} et al., ``Lie reductions and exact solutions of dispersionless Nizhnik equation'', Preprint, arXiv:2308.03744 [math-ph] (2023) Full Text: arXiv OA License
Boyko, Vyacheslav M.; Lokaziuk, Oleksandra V.; Popovych, Roman O. Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein-Gordon equations. (English) Zbl 1472.35019 Anal. Math. Phys. 11, No. 3, Paper No. 127, 38 p. (2021). MSC: 35B06 35L10 PDFBibTeX XMLCite \textit{V. M. Boyko} et al., Anal. Math. Phys. 11, No. 3, Paper No. 127, 38 p. (2021; Zbl 1472.35019) Full Text: DOI arXiv
Boyko, Vyacheslav M.; Kunzinger, Michael; Popovych, Roman O. Parameter-dependent linear ordinary differential equations and topology of domains. (English) Zbl 1465.34016 J. Differ. Equations 284, 546-575 (2021). MSC: 34A30 34A05 34A12 PDFBibTeX XMLCite \textit{V. M. Boyko} et al., J. Differ. Equations 284, 546--575 (2021; Zbl 1465.34016) Full Text: DOI arXiv
Boyko, Vyacheslav M.; Lokaziuk, Oleksandra V.; Popovych, Roman O. Admissible transformations and Lie symmetries of linear systems of second-order ordinary differential equations. arXiv:2105.05139 Preprint, arXiv:2105.05139 [math.CA] (2021). MSC: 34C14 34A30 34A26 BibTeX Cite \textit{V. M. Boyko} et al., ``Admissible transformations and Lie symmetries of linear systems of second-order ordinary differential equations'', Preprint, arXiv:2105.05139 [math.CA] (2021) Full Text: arXiv OA License
Opanasenko, Stanislav; Boyko, Vyacheslav; Popovych, Roman O. Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity. (English) Zbl 1430.35011 J. Math. Anal. Appl. 484, No. 1, Article ID 123739, 30 p. (2020). MSC: 35B06 35K57 35C05 PDFBibTeX XMLCite \textit{S. Opanasenko} et al., J. Math. Anal. Appl. 484, No. 1, Article ID 123739, 30 p. (2020; Zbl 1430.35011) Full Text: DOI arXiv
Boyko, Vaycheslav M.; Kunzinger, Michael; Popovych, Roman O. Singular reduction modules of differential equations. (English) Zbl 1368.35014 J. Math. Phys. 57, No. 10, 101503, 34 p. (2016). MSC: 35B06 35C05 PDFBibTeX XMLCite \textit{V. M. Boyko} et al., J. Math. Phys. 57, No. 10, 101503, 34 p. (2016; Zbl 1368.35014) Full Text: DOI arXiv
Boyko, Vyacheslav M.; Popovych, Roman O.; Shapoval, Nataliya M. Equivalence groupoids of classes of linear ordinary differential equations and their group classification. arXiv:1403.6062 Preprint, arXiv:1403.6062 [math.CA] (2014). MSC: 34C14 34A30 BibTeX Cite \textit{V. M. Boyko} et al., ``Equivalence groupoids of classes of linear ordinary differential equations and their group classification'', Preprint, arXiv:1403.6062 [math.CA] (2014) Full Text: DOI arXiv OA License
Boyko, Vyacheslav M.; Popovych, Roman O. Reduction operators of the linear rod equation. (English) Zbl 1292.35163 Vaneeva, O. O. (ed.) et al., Proceedings of the 6th international workshop on group analysis of differential equations and integrable systems, Protaras, Cyprus, June 17–21, 2012. Nicosia: University of Cyprus, Department of Mathematics and Statistics (ISBN 978-9963-700-63-9/pbk). 17-29 (2013). MSC: 35L25 74K10 35B06 PDFBibTeX XMLCite \textit{V. M. Boyko} and \textit{R. O. Popovych}, in: Proceedings of the 6th international workshop on group analysis of differential equations and integrable systems, Protaras, Cyprus, June 17--21, 2012. Nicosia: University of Cyprus, Department of Mathematics and Statistics. 17--29 (2013; Zbl 1292.35163)
Bojko, V. M.; Popovych, R. O. Conditional symmetries of the linear rod equation. (Ukrainian. English summary) Zbl 1289.35319 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2013, No. 9, 7-15 (2013). MSC: 35Q74 35B06 74K10 PDFBibTeX XMLCite \textit{V. M. Bojko} and \textit{R. O. Popovych}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2013, No. 9, 7--15 (2013; Zbl 1289.35319)
Vaneeva, O. O. (ed.); Sophocleous, Christodoulos (ed.); Popovych, R. O. (ed.); Leach, P. G. L. (ed.); Boyko, V. M. (ed.); Damianou, Pantelis (ed.) Proceedings of the 6th international workshop on group analysis of differential equations and integrable systems, Protaras, Cyprus, June 17–21, 2012. (English) Zbl 1264.35004 Nicosia: University of Cyprus, Department of Mathematics and Statistics (ISBN 978-9963-700-63-9/pbk). 248 p. (2013). MSC: 35-06 37-06 00B25 35Qxx 37Jxx 37Nxx PDFBibTeX XMLCite \textit{O. O. Vaneeva} (ed.) et al., Proceedings of the 6th international workshop on group analysis of differential equations and integrable systems, Protaras, Cyprus, June 17--21, 2012. Nicosia: University of Cyprus, Department of Mathematics and Statistics (2013; Zbl 1264.35004) Full Text: Link
Boyko, Vyacheslav M.; Popovych, Roman O.; Shapoval, Nataliya M. Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients. (English) Zbl 1260.34064 J. Math. Anal. Appl. 397, No. 1, 434-440 (2013). Reviewer: Oleg V. Makeev (Ulyanovsk) MSC: 34C14 34A30 PDFBibTeX XMLCite \textit{V. M. Boyko} et al., J. Math. Anal. Appl. 397, No. 1, 434--440 (2013; Zbl 1260.34064) Full Text: DOI arXiv
Bojko, V. M.; Popovych, R. O. Potential conservation laws of linear evolution equations with single potential. (Ukrainian. English summary) Zbl 1249.35011 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2012, No. 4, 7-14 (2012). MSC: 35B06 35L65 35A30 35F05 35G05 PDFBibTeX XMLCite \textit{V. M. Bojko} and \textit{R. O. Popovych}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2012, No. 4, 7--14 (2012; Zbl 1249.35011)
Boyko, Vyacheslav M.; Popovych, Roman O. Simplest potential conservation laws of linear evolution equations. (English) Zbl 1234.35015 Ivanova, Nataliya (ed.) et al., Proceedings of the 5th international workshop on group analysis of differential equations and integrable systems, Protaras, Cyprus, June 6–10, 2011. Nicosia: University of Cyprus, Department of Mathematics and Statistics (ISBN 978-9963-700-07-3/pbk). 28-39 (2011). MSC: 35B06 35L65 35A30 35F05 35G05 PDFBibTeX XMLCite \textit{V. M. Boyko} and \textit{R. O. Popovych}, in: Proceedings of the 5th international workshop on group analysis of differential equations and integrable systems, Protaras, Cyprus, June 6--10, 2011. Nicosia: University of Cyprus, Department of Mathematics and Statistics. 28--39 (2011; Zbl 1234.35015) Full Text: arXiv
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman Invariants of Lie algebras via moving frames. (English) Zbl 1251.17006 Ivanova, Nataliya (ed.) et al., Proceedings of the 4th international workshop (GADEIS-IV) on group analysis of differential equations and integrable systems, Protaras, Cyprus, October 26–30, 2008. Nicosia: University of Cyprus, Department of Mathematics and Statistics (ISBN 978-9963-689-12-5). 36-44 (2009). MSC: 17B35 17B08 PDFBibTeX XMLCite \textit{V. Boyko} et al., in: Proceedings of the 4th international workshop (GADEIS-IV) on group analysis of differential equations and integrable systems, Protaras, Cyprus, October 26--30, 2008. Nicosia: University of Cyprus, Department of Mathematics and Statistics. 36--44 (2009; Zbl 1251.17006) Full Text: arXiv
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements. (English) Zbl 1168.17005 Linear Algebra Appl. 428, No. 4, 834-854 (2008). Reviewer: Rutwig Campoamor-Stursberg (Madrid) MSC: 17B05 17B10 17B30 22E70 58D19 81R05 PDFBibTeX XMLCite \textit{V. Boyko} et al., Linear Algebra Appl. 428, No. 4, 834--854 (2008; Zbl 1168.17005) Full Text: DOI arXiv
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman Invariants of triangular Lie algebras with one nil-independent diagonal element. (English) Zbl 1185.17008 J. Phys. A, Math. Theor. 40, No. 32, 9783-9792 (2007). MSC: 17B30 81R05 PDFBibTeX XMLCite \textit{V. Boyko} et al., J. Phys. A, Math. Theor. 40, No. 32, 9783--9792 (2007; Zbl 1185.17008) Full Text: DOI arXiv
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman Invariants of triangular Lie algebras. (English) Zbl 1121.17008 J. Phys. A, Math. Theor. 40, No. 27, 7557-7572 (2007). Reviewer: Rutwig Campoamor-Stursberg (Madrid) MSC: 17B30 81R05 PDFBibTeX XMLCite \textit{V. Boyko} et al., J. Phys. A, Math. Theor. 40, No. 27, 7557--7572 (2007; Zbl 1121.17008) Full Text: DOI arXiv
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman Invariants of Lie algebras with fixed structure of nilradicals. (English) Zbl 1183.17003 J. Phys. A, Math. Theor. 40, No. 1, 113-130 (2007). MSC: 17B30 17B10 PDFBibTeX XMLCite \textit{V. Boyko} et al., J. Phys. A, Math. Theor. 40, No. 1, 113--130 (2007; Zbl 1183.17003) Full Text: DOI arXiv
Boyko, V. M. (ed.); Nikitin, A. G. (ed.); Popovych, R. O. (ed.) Symmetry and integrability of equations of mathematical physics. (Ukrainian, English, Russian. English summary) Zbl 1150.35001 Zb. Pr. Inst. Mat. NAN Ukr. 3, No. 2, 400 p. (2006). Reviewer: I. A. Yehorchenko (Kyiv) MSC: 35-06 00B30 35A30 58J70 PDFBibTeX XMLCite \textit{V. M. Boyko} (ed.) et al., Zb. Pr. Inst. Mat. NAN Ukr. 3, No. 2, 400 p. (2006; Zbl 1150.35001) Full Text: Link
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman Computation of invariants of Lie algebras by means of moving frames. (English) Zbl 1106.17040 J. Phys. A, Math. Gen. 39, No. 20, 5749-5762 (2006). MSC: 17B81 17B30 81R05 PDFBibTeX XMLCite \textit{V. Boyko} et al., J. Phys. A, Math. Gen. 39, No. 20, 5749--5762 (2006; Zbl 1106.17040) Full Text: DOI arXiv
Nikitin, A. G. (ed.); Bojko, V. M. (ed.); Popovych, R. O. (ed.); Jegorchenko, I. A. (ed.) Proceedings of the fifth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, June 23–29, 2003. Part 3. (English) Zbl 1088.17002 Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine. Mathematics and its Applications. 50(3). Kyïv: Institute of Mathematics of NAS of Ukraine (ISBN 966-02-3227-6). 504 p. (2004). MSC: 17-06 20-06 81-06 00B25 PDFBibTeX XMLCite \textit{A. G. Nikitin} (ed.) et al., Proceedings of the fifth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, June 23--29, 2003. Part 3. Kyïv: Institute of Mathematics of NAS of Ukraine (2004; Zbl 1088.17002)
Nikitin, A. G. (ed.); Bojko, V. M. (ed.); Popovych, R. O. (ed.); Jegorchenko, I. A. (ed.) Proceedings of the fifth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, June 23–29, 2003. Part 2. (English) Zbl 1088.17001 Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine. Mathematics and its Applications. 50(2). Kyïv: Institute of Mathematics of NAS of Ukraine (ISBN 966-02-3226-8). 504 p. (2004). MSC: 17-06 81-06 00B25 PDFBibTeX XMLCite \textit{A. G. Nikitin} (ed.) et al., Proceedings of the fifth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, June 23--29, 2003. Part 2. Kyïv: Institute of Mathematics of NAS of Ukraine (2004; Zbl 1088.17001)
Nikitin, A. G. (ed.); Bojko, V. M. (ed.); Popovych, R. O. (ed.); Jegorchenko, I. A. (ed.) Proceedings of the fifth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, June 23–29, 2003. Part 1. (English) Zbl 1088.34002 Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine. Mathematics and its Applications. 50(1). Kyïv: Institute of Mathematics of NAS of Ukraine (ISBN 966-02-3225-X). 524 p. (2004). MSC: 34-06 35-06 37-06 00B25 PDFBibTeX XMLCite \textit{A. G. Nikitin} (ed.) et al., Proceedings of the fifth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, June 23--29, 2003. Part 1. Kyïv: Institute of Mathematics of NAS of Ukraine (2004; Zbl 1088.34002)
Popovych, Roman O.; Boyko, Vyacheslav M.; Nesterenko, Maryna O.; Lutfullin, Maxim W. Realizations of real low-dimensional Lie algebras. (English) Zbl 1040.17021 J. Phys. A, Math. Gen. 36, No. 26, 7337-7360 (2003). MSC: 17B66 34M15 PDFBibTeX XMLCite \textit{R. O. Popovych} et al., J. Phys. A, Math. Gen. 36, No. 26, 7337--7360 (2003; Zbl 1040.17021) Full Text: DOI arXiv
Popovych, Roman O.; Boyko, Vyacheslav M. Differential invariants and application to Riccati-type systems. (English) Zbl 1044.53012 Nikitin, A. G. (ed.) et al., Proceedings of the fourth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, July 9–15, 2001. Part 1. Dedicated to the 200th anniversary of M. Ostrohrads’kyi. Kyïv: Institute of Mathematics of NAS of Ukraine (ISBN 966-02-2486-9). Proc. Inst. Math. Natl. Acad. Sci. Ukr., Math. Appl. 43(1), 184-193 (2002). Reviewer: A. G. Sergyeyev (Kyïv) MSC: 53A55 22E05 58J70 34A26 35A30 PDFBibTeX XMLCite \textit{R. O. Popovych} and \textit{V. M. Boyko}, in: Proceedings of the fourth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, July 9--15, 2001. Part 1. Dedicated to the 200th anniversary of M. Ostrohrads'kyi. Kyïv: Institute of Mathematics of NAS of Ukraine. 184--193 (2002; Zbl 1044.53012) Full Text: arXiv
Nikitin, A. G. (ed.); Bojko, V. M. (ed.); Popovych, R. O. (ed.) Proceedings of the fourth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, July 9–15, 2001. Part 2. Dedicated to the 200th anniversary of M. Ostrohrads’kyi. (English) Zbl 0989.00035 Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine. Mathematics and its Applications. 43(2). Kyïv: Institute of Mathematics of NAS of Ukraine. 403-784 (2002). MSC: 00B25 17-06 81-06 PDFBibTeX XMLCite \textit{A. G. Nikitin} (ed.) et al., Proceedings of the fourth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, July 9--15, 2001. Part 2. Dedicated to the 200th anniversary of M. Ostrohrads'kyi. Kyïv: Institute of Mathematics of NAS of Ukraine (2002; Zbl 0989.00035)
Nikitin, A. G. (ed.); Bojko, V. M. (ed.); Popovych, R. O. (ed.) Proceedings of the fourth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, July 9–15, 2001. Part 1. Dedicated to the 200th anniversary of M. Ostrohrads’kyi. (English) Zbl 0989.00037 Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine. Mathematics and its Applications. 43(1). Kyïv: Institute of Mathematics of NAS of Ukraine. 392 p. (2002). MSC: 00B25 34-06 35-06 37-06 PDFBibTeX XMLCite \textit{A. G. Nikitin} (ed.) et al., Proceedings of the fourth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, July 9--15, 2001. Part 1. Dedicated to the 200th anniversary of M. Ostrohrads'kyi. Kyïv: Institute of Mathematics of NAS of Ukraine (2002; Zbl 0989.00037)
Boyko, V. M.; Popovych, R. O. Differential invariants of the one-parameter Lie groups. (English) Zbl 1003.35014 Nikitin, A. G. (ed.), Group and analytic methods in mathematical physics. Kyïv: Instytut Matematyky NAN Ukraïny. Pr. Inst. Mat. Nats. Akad. Nauk Ukr., Mat. Zastos. 36, 51-62 (2001). Reviewer: A.N.Kochubei (Kyïv) MSC: 35A30 22E05 PDFBibTeX XMLCite \textit{V. M. Boyko} and \textit{R. O. Popovych}, in: Grupovi ta analitychni metody v matematichnij fizytsi. Kyïv: Instytut Matematyky NAN Ukraïny. 51--62 (2001; Zbl 1003.35014)
Bojko, V. M.; Popovych, R. O. On differential invariants in the space of two variables. (Ukrainian. English summary) Zbl 0981.58027 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2001, No. 5, 7-10 (2001). MSC: 58J70 PDFBibTeX XMLCite \textit{V. M. Bojko} and \textit{R. O. Popovych}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2001, No. 5, 7--10 (2001; Zbl 0981.58027)