Koval, Serhii D.; Bihlo, Alexander; Popovych, Roman O. Extended symmetry analysis of remarkable (1+2)-dimensional Fokker-Planck equation. (English) Zbl 1522.35023 Eur. J. Appl. Math. 34, No. 5, 1067-1098 (2023). MSC: 35B06 35Q84 35A30 35C05 35C06 35K10 35K70 PDFBibTeX XMLCite \textit{S. D. Koval} et al., Eur. J. Appl. Math. 34, No. 5, 1067--1098 (2023; Zbl 1522.35023) Full Text: DOI arXiv
Opanasenko, Stanislav; Popovych, Roman O. Mapping method of group classification. (English) Zbl 1487.35023 J. Math. Anal. Appl. 513, No. 2, Article ID 126209, 43 p. (2022). MSC: 35B06 35K10 35Q84 PDFBibTeX XMLCite \textit{S. Opanasenko} and \textit{R. O. Popovych}, J. Math. Anal. Appl. 513, No. 2, Article ID 126209, 43 p. (2022; Zbl 1487.35023) Full Text: DOI arXiv
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
Yourdkhany, Mahdieh; Nadjafikhah, Mehdi; Toomanian, Megerdich Preliminary group classification and some exact solutions of the 2-Hessian equation. (English) Zbl 1470.35023 Bull. Iran. Math. Soc. 47, No. 4, 977-994 (2021). MSC: 35B06 35A30 35J60 17B66 53C10 53C12 76M60 58J70 PDFBibTeX XMLCite \textit{M. Yourdkhany} et al., Bull. Iran. Math. Soc. 47, No. 4, 977--994 (2021; Zbl 1470.35023) Full Text: DOI arXiv
Opanasenko, Stanislav; Bihlo, Alexander; Popovych, Roman O.; Sergyeyev, Artur Extended symmetry analysis of an isothermal no-slip drift flux model. (English) Zbl 1453.76186 Physica D 402, Article ID 132188, 16 p. (2020). MSC: 76M60 35B06 PDFBibTeX XMLCite \textit{S. Opanasenko} et al., Physica D 402, Article ID 132188, 16 p. (2020; Zbl 1453.76186) Full Text: DOI arXiv
Vaneeva, Olena O.; Bihlo, Alexander; Popovych, Roman O. Generalization of the algebraic method of group classification with application to nonlinear wave and elliptic equations. (English) Zbl 1453.35011 Commun. Nonlinear Sci. Numer. Simul. 91, Article ID 105419, 28 p. (2020). MSC: 35B06 35L71 35J61 PDFBibTeX XMLCite \textit{O. O. Vaneeva} et al., Commun. Nonlinear Sci. Numer. Simul. 91, Article ID 105419, 28 p. (2020; Zbl 1453.35011) Full Text: DOI arXiv
Opanasenko, Stanislav; Bihlo, Alexander; Popovych, Roman O. Equivalence groupoid and group classification of a class of variable-coefficient Burgers equations. (English) Zbl 1447.35020 J. Math. Anal. Appl. 491, No. 1, Article ID 124215, 21 p. (2020). MSC: 35B06 35A22 35K58 PDFBibTeX XMLCite \textit{S. Opanasenko} et al., J. Math. Anal. Appl. 491, No. 1, Article ID 124215, 21 p. (2020; Zbl 1447.35020) Full Text: DOI arXiv
Kurujyibwami, Célestin; Basarab-Horwath, Peter; Popovych, Roman O. Algebraic method for group classification of \((1+1)\)-dimensional linear Schrödinger equations. (English) Zbl 1409.35179 Acta Appl. Math. 157, No. 1, 171-203 (2018). MSC: 35Q41 35B06 35A30 PDFBibTeX XMLCite \textit{C. Kurujyibwami} et al., Acta Appl. Math. 157, No. 1, 171--203 (2018; Zbl 1409.35179) Full Text: DOI arXiv
Grigor’ev, Yu. N.; Meleshko, S. V.; Suriyawichitseranee, A. Exact solutions of the Boltzmann equations with a source. (English. Russian original) Zbl 1393.35139 J. Appl. Mech. Tech. Phys. 59, No. 2, 189-196 (2018); translation from Prikl. Mekh. Tekh. Fiz. 59, No. 2, 3-11 (2018). MSC: 35Q20 35C05 PDFBibTeX XMLCite \textit{Yu. N. Grigor'ev} et al., J. Appl. Mech. Tech. Phys. 59, No. 2, 189--196 (2018; Zbl 1393.35139); translation from Prikl. Mekh. Tekh. Fiz. 59, No. 2, 3--11 (2018) Full Text: DOI
Long, Feng-Shan; Karnbanjong, Adisak; Suriyawichitseranee, Amornrat; Grigoriev, Yurii N.; Meleshko, Sergey V. Application of a Lie group admitted by a homogeneous equation for group classification of a corresponding inhomogeneous equation. (English) Zbl 1459.76112 Commun. Nonlinear Sci. Numer. Simul. 48, 350-360 (2017). MSC: 76M60 35Q35 35A30 PDFBibTeX XMLCite \textit{F.-S. Long} et al., Commun. Nonlinear Sci. Numer. Simul. 48, 350--360 (2017; Zbl 1459.76112) Full Text: DOI
Opanasenko, Stanislav; Bihlo, Alexander; Popovych, Roman O. Group analysis of general Burgers-Korteweg-de Vries equations. (English) Zbl 1375.35457 J. Math. Phys. 58, No. 8, 081511, 37 p. (2017). MSC: 35Q53 35B06 22E70 PDFBibTeX XMLCite \textit{S. Opanasenko} et al., J. Math. Phys. 58, No. 8, 081511, 37 p. (2017; Zbl 1375.35457) Full Text: DOI arXiv
Bihlo, Alexander; Popovych, Roman O. Group classification of linear evolution equations. (English) Zbl 1368.35013 J. Math. Anal. Appl. 448, No. 2, 982-1005 (2017). MSC: 35B06 PDFBibTeX XMLCite \textit{A. Bihlo} and \textit{R. O. Popovych}, J. Math. Anal. Appl. 448, No. 2, 982--1005 (2017; Zbl 1368.35013) Full Text: DOI arXiv
Wang, Gangwei; Kara, A. H. Nonlocal symmetry analysis, explicit solutions and conservation laws for the fourth-order Burgers’ equation. (English) Zbl 1355.35154 Chaos Solitons Fractals 81, Part A, 290-298 (2015). MSC: 35Q35 35B06 35C05 70S10 PDFBibTeX XMLCite \textit{G. Wang} and \textit{A. H. Kara}, Chaos Solitons Fractals 81, Part A, 290--298 (2015; Zbl 1355.35154) Full Text: DOI
Siriwat, P.; Kaewmanee, C.; Meleshko, S. V. Group classification of one-dimensional nonisentropic equations of fluids with internal inertia. II: General case. (English) Zbl 1341.58024 Contin. Mech. Thermodyn. 27, No. 3, 447-460 (2015). MSC: 58J70 35Q35 76M60 76T10 35A30 PDFBibTeX XMLCite \textit{P. Siriwat} et al., Contin. Mech. Thermodyn. 27, No. 3, 447--460 (2015; Zbl 1341.58024) Full Text: DOI
Suksern, S.; Moyo, S.; Meleshko, S. V. Application of group analysis to classification of systems of three second-order ordinary differential equations. (English) Zbl 1344.34047 Math. Methods Appl. Sci. 38, No. 18, 5097-5113 (2015). Reviewer: Charis Harley (Johannesburg) MSC: 34C14 34A30 22E60 34C20 PDFBibTeX XMLCite \textit{S. Suksern} et al., Math. Methods Appl. Sci. 38, No. 18, 5097--5113 (2015; Zbl 1344.34047) Full Text: DOI arXiv
Mkhize, T. G.; Moyo, S.; Meleshko, S. V. Complete group classification of systems of two linear second-order ordinary differential equations: the algebraic approach. (English) Zbl 1338.34076 Math. Methods Appl. Sci. 38, No. 9, 1824-1837 (2015). Reviewer: Jinzhi Lei (Beijing) MSC: 34C14 34C20 22E60 34A30 PDFBibTeX XMLCite \textit{T. G. Mkhize} et al., Math. Methods Appl. Sci. 38, No. 9, 1824--1837 (2015; Zbl 1338.34076) Full Text: DOI
Bozhkov, Y.; Dimas, S. Group classification of a generalized Black-Scholes-Merton equation. (English) Zbl 1457.91422 Commun. Nonlinear Sci. Numer. Simul. 19, No. 7, 2200-2211 (2014). MSC: 91G80 35A30 35K58 PDFBibTeX XMLCite \textit{Y. Bozhkov} and \textit{S. Dimas}, Commun. Nonlinear Sci. Numer. Simul. 19, No. 7, 2200--2211 (2014; Zbl 1457.91422) Full Text: DOI arXiv
Szatmari, Simon; Bihlo, Alexander Symmetry analysis of a system of modified shallow-water equations. (English) Zbl 1470.76022 Commun. Nonlinear Sci. Numer. Simul. 19, No. 3, 530-537 (2014). MSC: 76B03 76M60 PDFBibTeX XMLCite \textit{S. Szatmari} and \textit{A. Bihlo}, Commun. Nonlinear Sci. Numer. Simul. 19, No. 3, 530--537 (2014; Zbl 1470.76022) Full Text: DOI arXiv
Bozhkov, Y.; Dimas, S. Group classification of a generalization of the Heath equation. (English) Zbl 1335.35005 Appl. Math. Comput. 243, 121-131 (2014). MSC: 35A30 35K10 PDFBibTeX XMLCite \textit{Y. Bozhkov} and \textit{S. Dimas}, Appl. Math. Comput. 243, 121--131 (2014; Zbl 1335.35005) Full Text: DOI arXiv
Bihlo, Alexander; Dos Santos Cardoso-Bihlo, Elsa; Popovych, Roman O. Invariant parameterization and turbulence modeling on the beta-plane. (English) Zbl 1302.76078 Physica D 269, 48-62 (2014). MSC: 76F30 35Q53 35A30 PDFBibTeX XMLCite \textit{A. Bihlo} et al., Physica D 269, 48--62 (2014; Zbl 1302.76078) Full Text: DOI arXiv
Bihlo, Alexander; Bluman, George Conservative parameterization schemes. (English) Zbl 1285.86003 J. Math. Phys. 54, No. 8, 083101, 24 p. (2013). MSC: 86A10 35Q86 76F65 35Q35 PDFBibTeX XMLCite \textit{A. Bihlo} and \textit{G. Bluman}, J. Math. Phys. 54, No. 8, 083101, 24 p. (2013; Zbl 1285.86003) Full Text: DOI arXiv
Bihlo, Alexander; Dos Santos Cardoso-Bihlo, Elsa; Popovych, Roman O. Complete group classification of a class of nonlinear wave equations. (English) Zbl 1282.35020 J. Math. Phys. 53, No. 12, 123515, 32 p. (2012). MSC: 35B06 35L70 35Q53 22E65 PDFBibTeX XMLCite \textit{A. Bihlo} et al., J. Math. Phys. 53, No. 12, 123515, 32 p. (2012; Zbl 1282.35020) Full Text: DOI arXiv
Popovych, Roman O.; Bihlo, Alexander Symmetry preserving parameterization schemes. (English) Zbl 1277.58021 J. Math. Phys. 53, No. 7, 073102, 36 p. (2012). MSC: 58J70 20G45 22E70 PDFBibTeX XMLCite \textit{R. O. Popovych} and \textit{A. Bihlo}, J. Math. Phys. 53, No. 7, 073102, 36 p. (2012; Zbl 1277.58021) Full Text: DOI arXiv
Vaneeva, Olena Lie symmetries and exact solutions of variable coefficient mKdV equations: an equivalence based approach. (English) Zbl 1245.35114 Commun. Nonlinear Sci. Numer. Simul. 17, No. 2, 611-618 (2012). MSC: 35Q53 35A22 35B06 PDFBibTeX XMLCite \textit{O. Vaneeva}, Commun. Nonlinear Sci. Numer. Simul. 17, No. 2, 611--618 (2012; Zbl 1245.35114) Full Text: DOI arXiv