A Lagrangian Description of the Higher-Order Painlevé Equations

Details A Lagrangian Description of the Higher-Order Painlevé Equations A Lagrangian Description of the Higher-Order Painlevé Equations

2012-01-18

arxiv.org/abs/1201.3703v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, to be published in Applied Mathematics and Computation

Scientific paper

We derive the Lagrangians of the higher-order Painlev\'e equations using
Jacobi's last multiplier technique. Some of these higher-order differential
equations display certain remarkable properties like passing the Painlev\'e
test and satisfy the conditions stated by Jur\'a$\check{s}$, (Acta Appl. Math.
66 (2001) 25--39), thus allowing for a Lagrangian description.

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