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

Tom 94 / 2011

Henryk Żołądek Banach Center Publications 94 (2011), 295-302 MSC: Primary 34M55; Secondary 37J30. DOI: 10.4064/bc94-0-20

Streszczenie

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 $\mathbb{C}^4$. 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.

Autorzy

  • Henryk ŻołądekInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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