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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}
}