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

• Autorzy: Henryk Żołądek
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 34M55: Painlev\'e and other special equations; classification, hierarchies;
• 37J30: Obstructions to integrability (nonintegrability criteria)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 94
• Numer: 1
• Strony: 295-302

Daty

wydano

2011

Twórcy

autor

Henryk Żołądek

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/bc94-0-20