A novel procedure to reduce by four the order of Euler-Lagrange equations associated to nth order variational problems involving single variable integrals is presented. In preparation, a new formula for the commutator of two C∞-symmetries is established. The method is based on a pair of variational C∞-symmetries whose commutators satisfy a certain solvability condition. It allows one to recover a (2n - 2)-parameter family of solutions for the original 2nth order Euler-Lagrange equation by solving two successive first order ordinary differential equations from the solution of the reduced Euler-Lagrange equation. The procedure is illustrated by two different examples.
|Original language||English (US)|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|State||Published - Mar 8 2018|
Bibliographical noteFunding Information:
A R and C M acknowledge financial support from the University of Cádiz and from Junta de Andalucía to the research group FQM 377.
A R acknowledges financial support from the Ministry of Education, Culture and Sport of Spain (FPU grant FPU15/02872) and from a grant of the University of Cádiz program ‘Movilidad Internacional, Becas UCA-Internacional Posgrado 2016–2017’ during his stay at the University of Minnesota.
© 2018 IOP Publishing Ltd.
- Euler-Lagrange equation
- solvability condition
- variational C-symmetry
- variational problem