A Lagrangian description of the higher-order Painlevé equations

A. Ghose Choudhury, Partha Guha, Nikolay A. Kudryashov

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We derive the Lagrangians of the higher-order Painlevé equations using Jacobi's last multiplier technique. Some of these higher-order differential equations display certain remarkable properties like passing the Painlevé test and satisfy the conditions stated by Juráš [M. Juráš, The inverse problem of the calculus of variations for sixth- and eighth-order scalar ordinary differential equations, Acta Appl. Math. 66 (1) (2001) 25-39], thus allowing for a Lagrangian description.

Original languageBritish English
Pages (from-to)6612-6619
Number of pages8
JournalApplied Mathematics and Computation
Issue number11
StatePublished - 5 Feb 2012


  • Higher-order Painlevé equation
  • Juráš conditions
  • Lagrangian
  • Painlevé test


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