Geodesic
On differential-invariant solutions
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 3, pp. 75-84 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

New results about automorphic systems obtained in last years using for constructions differential-invariant solutions. Method of classification of differential-invariant submodels offered.
Keywords: Lie symmetries, automorphic systems, differential invariants, differential-invariants solutions. 
@article{VNGU_2016_16_3_a6,
     author = {A. A. Talyshev},
     title = {On differential-invariant solutions},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {75--84},
     year = {2016},
     volume = {16},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2016_16_3_a6/}
}
TY  - JOUR
AU  - A. A. Talyshev
TI  - On differential-invariant solutions
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2016
SP  - 75
EP  - 84
VL  - 16
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VNGU_2016_16_3_a6/
LA  - ru
ID  - VNGU_2016_16_3_a6
ER  - 
%0 Journal Article
%A A. A. Talyshev
%T On differential-invariant solutions
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2016
%P 75-84
%V 16
%N 3
%U http://geodesic.mathdoc.fr/item/VNGU_2016_16_3_a6/
%G ru
%F VNGU_2016_16_3_a6
A. A. Talyshev. On differential-invariant solutions. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 3, pp. 75-84. http://geodesic.mathdoc.fr/item/VNGU_2016_16_3_a6/

[1] L. V. Ovsyannikov, Group Analysis of Differential Equations, Academic Press, New York, 1982

[2] A. A. Talyshev, “On automorphic systems of finite-dimensional Lie groups”, Ufa Math. J., 4:4 (2012), 127–134

[3] A. A. Talyshev, “On integration of automorphic systems of finite-dimensional Lie groups”, Ufa Math. J., 6:1 (2014), 104–110 | DOI

[4] A. A. Talyshev, “Building the basis of differential invariants of finite-dimensional Lie groups using computer algebra”, Proc. of the Int. Conf. “Modern Problems of Mathematics, Informatics, and Bioinformatics,” dedicated to the $100^\text{th}$ Anniversary of the birthday A. A. Lyapunov (Novosibirsk, Russia, October 11–14, 2011) (in Russian)

[5] S. V. Habirov, “Classification of differential invariant submodels”, Sib. Mat. Zh., 45:3 (2004), 682–701 (in Russian)

[6] S. V. Golovin, “Group foliation and exact equations of transonic gas motion”, Appl. Mech. Tech. Phys., 44:3 (2003), 51–63 (in Russian)

[7] A. A. Talyshev, “On symmetries of non-involutive systems”, Proc. of the Int. Conf. “Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Practice”, dedicated to the $90^\text{th}$ anniversary of N. N. Yanenko (in Russian)

[8] L. V. Ovsyannikov, “On ‘simple’ solutions of equations of polytropic gas dynemics”, Appl. Mech. Tech. Phys., 40:2 (1999), 5–12 (in Russian)

[9] L. V. Ovsyannikov, “Programm submodels. Gas dynamics”, Appl. Math. and Mech., 58:4 (1994), 30–55 (in Russian)

[10] L. V. Ovsyannikov, “On hierarchy of invariant submodels of differential equations”, Dokl. Ross. Akad. Nauk, 361:6 (1998), 740–742 (in Russian)

[11] K. K. Izmaylova, A. P. Chupakhin, “Group theoretical solutions of Schrödinger equation generated by three-dimensional symmetry algebras”, Nelin. Dinam., 3:3 (2007), 349–362 (in Russian)