Internal Lagrangians of PDEs as variational principles

A description of how the principle of stationary action reproduces itself in terms of the intrinsic geometry of variational equations is proposed. A notion of stationary points of an internal Lagrangian is introduced. A connection between symmetries, conservation laws and internal Lagrangians is est...

Full description

Saved in:
Bibliographic Details
Published in:Journal of geometry and physics 2024-05, Vol.199, p.105143, Article 105143
Main Author: Druzhkov, Kostya
Format: Article
Language:English
Subjects:
Internal Lagrangian
Noether's theorem
Presymplectic structure
Variational principle
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A description of how the principle of stationary action reproduces itself in terms of the intrinsic geometry of variational equations is proposed. A notion of stationary points of an internal Lagrangian is introduced. A connection between symmetries, conservation laws and internal Lagrangians is established. Noether's theorem is formulated in terms of internal Lagrangians. A relation between non-degenerate Lagrangians and the corresponding internal Lagrangians is investigated. Several examples are discussed.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2024.105143