A Lagrangian description of the higher-order Painleve equations

作者：Choudhury A Ghose; Guha Partha; Kudryashov Nikolay A^*

来源：Applied Mathematics and Computation, 2012, 218(11): 6612-6619.

DOI：10.1016/j.amc.2011.12.008

• Higher-order Painleve equation
• Painleve test
• Lagrangian, Juras conditions

We derive the Lagrangians of the higher-order Painleve equations using Jacobi's last multiplier technique. Some of these higher-order differential equations display certain remarkable properties like passing the Painleve test and satisfy the conditions stated by Juras [M. Juras, 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.

• 出版日期2012-2-5