The Geometry of Darboux Integrable Elliptic Systems
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910020315119616 |
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| author | Fels, Mark E. Ivey, Thomas A. |
| author_facet | Fels, Mark E. Ivey, Thomas A. |
| contents | We characterize real elliptic differential systems whose solutions can be expressed in terms of holomorphic solutions to an associated holomorphic Pfaffian system $\mathcal H$ on a complex manifold. In particular, these elliptic systems arise as quotients by a group $G$ of the real differential system generated by the real and imaginary parts of $\mathcal H$, such that $G$ is the real form of a complex Lie group $K$ which is a symmetry group of $\mathcal H$. Subject to some mild genericity assumptions, we show that such elliptic systems are characterized by a property known as Darboux integrability. Examples discussed include first- and second-order elliptic PDE and PDE systems in the plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19893 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Geometry of Darboux Integrable Elliptic Systems Fels, Mark E. Ivey, Thomas A. Differential Geometry Analysis of PDEs 35A30, 35C60, 35J60, 53A55, 53C15, 53C56, 58A15 We characterize real elliptic differential systems whose solutions can be expressed in terms of holomorphic solutions to an associated holomorphic Pfaffian system $\mathcal H$ on a complex manifold. In particular, these elliptic systems arise as quotients by a group $G$ of the real differential system generated by the real and imaginary parts of $\mathcal H$, such that $G$ is the real form of a complex Lie group $K$ which is a symmetry group of $\mathcal H$. Subject to some mild genericity assumptions, we show that such elliptic systems are characterized by a property known as Darboux integrability. Examples discussed include first- and second-order elliptic PDE and PDE systems in the plane. |
| title | The Geometry of Darboux Integrable Elliptic Systems |
| topic | Differential Geometry Analysis of PDEs 35A30, 35C60, 35J60, 53A55, 53C15, 53C56, 58A15 |
| url | https://arxiv.org/abs/2409.19893 |