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

Banach Center Publications (2011)

- Volume: 94, Issue: 1, page 295-302
- ISSN: 0137-6934

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topHenryk 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 -

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