A Lagrangian Description of the Higher-Order Painlevé Equations

preprint2012arXivOpen access

Abstract

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 Jurásˇ\check{s}, (Acta Appl. Math. 66 (2001) 25--39), thus allowing for a Lagrangian description.

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