Geodesic
The first integrals and rational solutions of differential equations with a moving singular line
Problemy fiziki, matematiki i tehniki, no. 1 (2019), pp. 72-77

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

The nonlinear autonomous higher-order differential equations with a moving singular line are studied. The first integrals of the Chazy equation and some other equations with a moving singular line are obtained. Nonlinear differential equations, for which general solutions are rational solutions of equations with a moving singular line are obtained. It is shown that with the help of Bäcklund transformations, rational solutions of equations with a movable singular line can be transformed into each other. Nonlinear differential equations of the second or third degree with respect to the highest derivative are obtained, for which these rational solutions are general solutions.
Keywords: differential equations, resonances, first integrals, Bäcklund transform, movable singular line.
Mots-clés : rational solutions 
@article{PFMT_2019_1_a13,
     author = {B. Zhang and Y. Chen and I. P. Martynov},
     title = {The first integrals and rational solutions of differential equations with a moving singular line},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {72--77},
     publisher = {mathdoc},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2019_1_a13/}
}
TY  - JOUR
AU  - B. Zhang
AU  - Y. Chen
AU  - I. P. Martynov
TI  - The first integrals and rational solutions of differential equations with a moving singular line
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2019
SP  - 72
EP  - 77
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2019_1_a13/
LA  - ru
ID  - PFMT_2019_1_a13
ER  - 
%0 Journal Article
%A B. Zhang
%A Y. Chen
%A I. P. Martynov
%T The first integrals and rational solutions of differential equations with a moving singular line
%J Problemy fiziki, matematiki i tehniki
%D 2019
%P 72-77
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2019_1_a13/
%G ru
%F PFMT_2019_1_a13
B. Zhang; Y. Chen; I. P. Martynov. The first integrals and rational solutions of differential equations with a moving singular line. Problemy fiziki, matematiki i tehniki, no. 1 (2019), pp. 72-77. http://geodesic.mathdoc.fr/item/PFMT_2019_1_a13/