Integration of first-order ODEs by Jacobi fields
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929329756176384 |
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| author | Pan-Collantes, A. J. Alvarez-Garcia, J. A. |
| author_facet | Pan-Collantes, A. J. Alvarez-Garcia, J. A. |
| contents | A new class of vector fields enabling the integration of first-order ordinary differential equations (ODEs) is introduced. These vector fields are not, in general, Lie point symmetries. The results are based on a relation between 2-dimensional Riemannian manifolds and the integrability of first-order ODEs, which was established in a previous work of the authors. An integration procedure is provided, together with several examples to illustrate it. A connection between integrating factors of first-order ODEs and Schrödinger-type equations is highlighted. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14352 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integration of first-order ODEs by Jacobi fields Pan-Collantes, A. J. Alvarez-Garcia, J. A. Classical Analysis and ODEs Differential Geometry A new class of vector fields enabling the integration of first-order ordinary differential equations (ODEs) is introduced. These vector fields are not, in general, Lie point symmetries. The results are based on a relation between 2-dimensional Riemannian manifolds and the integrability of first-order ODEs, which was established in a previous work of the authors. An integration procedure is provided, together with several examples to illustrate it. A connection between integrating factors of first-order ODEs and Schrödinger-type equations is highlighted. |
| title | Integration of first-order ODEs by Jacobi fields |
| topic | Classical Analysis and ODEs Differential Geometry |
| url | https://arxiv.org/abs/2404.14352 |