| Title | The point symmetry group of a system of free second-order equations |
| Publication Type | Journal Article |
| Year of Publication | 2014 |
| Authors | Shapoval, NM |
| Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
| DOI | 10.15407/dopovidi2014.06.032 |
| Issue | 6 |
| Section | Mathematics |
| Pagination | 32-36 |
| Date Published | 6/2014 |
| Language | Ukrainian |
| Abstract | It is proved that the complete point symmetry group of a system of free second-order ordinary differential equations is a projective general linear group acting in the space of independent and dependent variables. |
| Keywords | point symmetry, system of free equations |
1. Markus L. Group theory and differential equations. Minneapolis: Univ. of Minnesota, 1960.
2. Gonzalez-Gascon F., Gonzalez-Lopez A. J. Math. Phys., 1983, 24: 2006–2021. https://doi.org/10.1063/1.525960
3. Gonzalez-Lopez A. J. Math. Phys., 1988, 29: 1097–1105. https://doi.org/10.1063/1.527948
4. Merker J. Acta Appl. Math., 2006, 92: 125–207. https://doi.org/10.1007/s10440-006-9064-z
5. Lie S. Vorlesungen über Differentialgleichungen mit bekannten infinitesimalen Transformationen. Leipzig: Teubner, 1891.
6. Boyko V. M., Popovych R. O., Shapoval N. M. J. Math. Anal. Appl., 2013, 397: 434–440. https://doi.org/10.1016/j.jmaa.2012.06.030
7. Bihlo A., Popovych R. O. Point symmetry group of the barotropic vorticity equation. Proceedings of the 5th Workshop “Group Analysis of Differential Equations and Integrable Systems”, 2011: 15–27.
8. Hydon P. E. Eur. J. Appl. Math., 2000, 11: 515–527. https://doi.org/10.1017/S0956792500004204
9. Bihlo A., Popovych R. O. J. Math. Phys., 2011, 52: 033103. https://doi.org/10.1063/1.3567175
10. Dos Santos Cardoso-Bihlo E., Popovych R. O. J. Engrg. Math., 2013, 82: 31–38. https://doi.org/10.1007/s10665-012-9589-2
