Geodesic
Parametric Painlev\'e equations
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 22, Tome 398 (2012), pp. 145-161

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

The parametric Painlevé equations are those ODEs whose general solutions can be presented in the parametric form in terms of the Painlevé functions. Most of these ODEs do not possess the Painlevé property. By considering similarity solutions of the short pulse equation and its decoupled generalization we derive a non-trivial example of the parametric Painlevé equation related with the third Painlevé equation. We also discuss some analytic properties of this equation describing the structure of movable singularities. 
@article{ZNSL_2012_398_a7,
     author = {A. V. Kitaev},
     title = {Parametric {Painlev\'e} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {145--161},
     publisher = {mathdoc},
     volume = {398},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a7/}
}
TY  - JOUR
AU  - A. V. Kitaev
TI  - Parametric Painlev\'e equations
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2012
SP  - 145
EP  - 161
VL  - 398
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a7/
LA  - en
ID  - ZNSL_2012_398_a7
ER  - 
%0 Journal Article
%A A. V. Kitaev
%T Parametric Painlev\'e equations
%J Zapiski Nauchnykh Seminarov POMI
%D 2012
%P 145-161
%V 398
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a7/
%G en
%F ZNSL_2012_398_a7
A. V. Kitaev. Parametric Painlev\'e equations. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 22, Tome 398 (2012), pp. 145-161. http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a7/