On the Darboux integrability of the Painlevé II equations

Jaume Llibre, Claudia Valls

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)


© 2015 the authors. In this paper we prove the non-existence of Darboux first integrals for the Painlevé II equations, ż = 1 for all values of α complexes αn: n = 2,4,.}. These αn are real and larger than-1/2.
Original languageEnglish
Pages (from-to)60-75
JournalJournal of Nonlinear Mathematical Physics
Issue number1
Publication statusPublished - 1 Jan 2015


  • Darboux integrability
  • Hamiltonian systems
  • Painlevé transcendents


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