A simple proof of the non-integrability of the first and the second Painlevé equations

Henryk Żołądek. "A simple proof of the non-integrability of the first and the second Painlevé equations." Banach Center Publications 94.1 (2011): 295-302. <http://eudml.org/doc/281688>.

@article{HenrykŻołądek2011,
abstract = {The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.},
author = {Henryk Żołądek},
journal = {Banach Center Publications},
keywords = {Painlevé equations; integrability in Liouville-Arnold sense; equation in variations},
language = {eng},
number = {1},
pages = {295-302},
title = {A simple proof of the non-integrability of the first and the second Painlevé equations},
url = {http://eudml.org/doc/281688},
volume = {94},
year = {2011},
}

TY - JOUR
AU - Henryk Żołądek
TI - A simple proof of the non-integrability of the first and the second Painlevé equations
JO - Banach Center Publications
PY - 2011
VL - 94
IS - 1
SP - 295
EP - 302
AB - The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.
LA - eng
KW - Painlevé equations; integrability in Liouville-Arnold sense; equation in variations
UR - http://eudml.org/doc/281688
ER -