Geodesic
Group classification of second-order projective-type ODEs
Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 1, pp. 37-51.

Voir la notice de l'article provenant de la source Math-Net.Ru

Group classification with respect to admitted point transformation groups is implemented for second-order ordinary differential equations with cubic nonlinearity in the first-order derivative. The result is obtained with the use of invariants of the equivalence transformation group of the family of equations under consideration. The corresponding Riemannian metric is found for the equations that are the projection of a system of geodesics to a two-dimensional surface.
Mots-clés : transformation group, equivalence, invariant, group classification.
Keywords: symmetry 
@article{SJIM_2016_19_1_a3,
     author = {Yu. Yu. Bagderina},
     title = {Group classification of second-order projective-type {ODEs}},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {37--51},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2016_19_1_a3/}
}
TY  - JOUR
AU  - Yu. Yu. Bagderina
TI  - Group classification of second-order projective-type ODEs
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2016
SP  - 37
EP  - 51
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2016_19_1_a3/
LA  - ru
ID  - SJIM_2016_19_1_a3
ER  - 
%0 Journal Article
%A Yu. Yu. Bagderina
%T Group classification of second-order projective-type ODEs
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2016
%P 37-51
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2016_19_1_a3/
%G ru
%F SJIM_2016_19_1_a3
Yu. Yu. Bagderina. Group classification of second-order projective-type ODEs. Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 1, pp. 37-51. http://geodesic.mathdoc.fr/item/SJIM_2016_19_1_a3/

[1] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR

[2] Ovsyannikov L. V., “Gruppovaya klassifikatsiya uravnenii vida $y''=f(x,y)$”, Prikl. mekhanika i tekhn. fizika, 45:2 (2004), 5–10 | MR | Zbl

[3] Lie S., “Klassifikation und Integration von gewöhnlichen Differentialgleichungen zwischen $x,y$, die eine Gruppe von Transformationen gestatten. IV”, Arch. Math., 9 (1884), 431–448

[4] Babich M. V., Bordag L. A., “Projective differential geometrical structure of the Painlevé equations”, J. Differential Equations, 157:2 (1999), 452–485 | DOI | MR | Zbl

[5] Kartak V. V., Second order ODEs cubic in the first-order derivative with 2-dimensional symmetry algebra, 2013, arXiv: 1307.3327[math.CA]

[6] Phauk S., Group classification of second-order ordinary differential equations in the form of a cubic polynomial in the first-order derivative, Master Thesis, Suranaree Univ. Technology, 2012

[7] Bagderina Yu. Yu., “Invariants of a family of scalar second-order ordinary differential equations”, J. Phys. A: Math. Theor., 46:29 (2013), 295201 | DOI | MR | Zbl

[8] Lie S., Vorlesungen über Differentialgleichungen mit Bekannten Infinitesimalen Transformationen, BG Teubner, Leipzig, 1891 | Zbl