Geodesic
On exact solutions of a system of quasi-linear equations describing integrable geodesic flows on a surface
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 949-954

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

In this paper, for the first time, explicit solutions of a semi-Hamiltonian system of quasi-linear differential equations by the generalized hodograph method are found. These solutions define (local) metrics on a surface for which the geodesic flow has a polynomial in momenta integrals of the fourth degree.
Keywords: integrable geodesic flows, the generalized hodograph method. 
@article{SEMR_2019_16_a92,
     author = {G. Abdikalikova and A. E. Mironov},
     title = {On exact solutions of a system of quasi-linear equations describing integrable geodesic flows on a surface},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {949--954},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a92/}
}
TY  - JOUR
AU  - G. Abdikalikova
AU  - A. E. Mironov
TI  - On exact solutions of a system of quasi-linear equations describing integrable geodesic flows on a surface
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 949
EP  - 954
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a92/
LA  - ru
ID  - SEMR_2019_16_a92
ER  - 
%0 Journal Article
%A G. Abdikalikova
%A A. E. Mironov
%T On exact solutions of a system of quasi-linear equations describing integrable geodesic flows on a surface
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 949-954
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a92/
%G ru
%F SEMR_2019_16_a92
G. Abdikalikova; A. E. Mironov. On exact solutions of a system of quasi-linear equations describing integrable geodesic flows on a surface. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 949-954. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a92/