Internal Lagrangians of PDEs as variational principles
Mathematical Physics
2024-11-22 v2 Differential Geometry
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.2307.14175,
title = {Internal Lagrangians of PDEs as variational principles},
author = {Kostya Druzhkov},
journal= {arXiv preprint arXiv:2307.14175},
year = {2024}
}