Geodesic
Power-elliptic expansions of solutions to an ordinary differential equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 12, pp. 2206-2218

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

A rather general ordinary differential equation is considered that can be represented as a polynomial in variables and derivatives. For this equation, the concept of power-elliptic expansions of its solutions is introduced and a method for computing them is described. It is shown that such expansions of solutions exist for the first and second Painlevé equations. 
@article{ZVMMF_2012_52_12_a7,
     author = {A. D. Bruno},
     title = {Power-elliptic expansions of solutions to an ordinary differential equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2206--2218},
     publisher = {mathdoc},
     volume = {52},
     number = {12},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_12_a7/}
}
TY  - JOUR
AU  - A. D. Bruno
TI  - Power-elliptic expansions of solutions to an ordinary differential equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2012
SP  - 2206
EP  - 2218
VL  - 52
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_12_a7/
LA  - ru
ID  - ZVMMF_2012_52_12_a7
ER  - 
%0 Journal Article
%A A. D. Bruno
%T Power-elliptic expansions of solutions to an ordinary differential equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2012
%P 2206-2218
%V 52
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_12_a7/
%G ru
%F ZVMMF_2012_52_12_a7
A. D. Bruno. Power-elliptic expansions of solutions to an ordinary differential equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 12, pp. 2206-2218. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_12_a7/