Lepage Equivalents of Second-Order Euler–Lagrange Forms and the Inverse Problem of the Calculus of Variations

DOI

10.1142/S1402925109000194How to use a DOI?

Keywords

Second-order Euler–Lagrange equations; Euler–Lagrange form; Lepage form; Lepage equivalent of a Lagrangian; Lepage equivalent of an Euler–Lagrange form; inverse problem of the calculus of variations

Abstract

In the calculus of variations, Lepage (n + 1)-forms are closed differential forms, representing Euler–Lagrange equations. They are fundamental for investigation of variational equations by means of exterior differential systems methods, with important applications in Hamilton and Hamilton–Jacobi theory and theory of integration of variational equations. In this paper, Lepage equivalents of second-order Euler–Lagrange quasi-linear PDE's are characterised explicitly. A closed (n + 1)-form uniquely determined by the Euler–Lagrange form is constructed, and used to find a geometric solution of the inverse problem of the calculus of variations.

Copyright

© 2009 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Olga Krupková
AU  - Dana Smetanová
PY  - 2021
DA  - 2021/01/07
TI  - Lepage Equivalents of Second-Order Euler–Lagrange Forms and the Inverse Problem of the Calculus of Variations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 235
EP  - 250
VL  - 16
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925109000194
DO  - 10.1142/S1402925109000194
ID  - Krupková2021
ER  -