Internal Lagrangians of PDEs as variational principles
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929599320948736 |
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| author | Druzhkov, Kostya |
| author_facet | Druzhkov, Kostya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14175 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Internal Lagrangians of PDEs as variational principles Druzhkov, Kostya Mathematical Physics Differential Geometry 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. |
| title | Internal Lagrangians of PDEs as variational principles |
| topic | Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2307.14175 |