On the commutator of C-symmetries and the reduction of Euler-Lagrange equations

A. Ruiz, C. Muriel, P. J. Olver

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 languageEnglish (US)
Article number145202
JournalJournal of Physics A: Mathematical and Theoretical
Issue number14
StatePublished - Mar 8 2018

Bibliographical note

Funding 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.

Funding Information:
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.

Publisher Copyright:
© 2018 IOP Publishing Ltd.


  • Euler-Lagrange equation
  • Lagrangian
  • commutator
  • solvability condition
  • variational C-symmetry
  • variational problem


Dive into the research topics of 'On the commutator of C-symmetries and the reduction of Euler-Lagrange equations'. Together they form a unique fingerprint.

Cite this