Frölicher-Nijenhuis geometry and integrable matrix PDE systems
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916379418951680 |
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| author | Müller-Hoissen, Folkert |
| author_facet | Müller-Hoissen, Folkert |
| contents | Given two tensor fields of type (1,1) on a smooth n-dimensional manifold M, such that all their Frölicher-Nijenhuis brackets vanish, the algebra of differential forms on M becomes a bi-differential graded algebra. As a consequence, there are partial differential equation (PDE) systems associated with it, which arise as the integrability condition of a system of linear equations and possess a binary Darboux transformation to generate exact solutions. We recover chiral models and potential forms of the self-dual Yang-Mills, as well as corresponding generalizations to higher than four dimensions, and obtain new integrable non-autonomous nonlinear matrix PDEs and corresponding systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01328 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Frölicher-Nijenhuis geometry and integrable matrix PDE systems Müller-Hoissen, Folkert Exactly Solvable and Integrable Systems Mathematical Physics Differential Geometry 37K10, 35Qxx, 53Z05 Given two tensor fields of type (1,1) on a smooth n-dimensional manifold M, such that all their Frölicher-Nijenhuis brackets vanish, the algebra of differential forms on M becomes a bi-differential graded algebra. As a consequence, there are partial differential equation (PDE) systems associated with it, which arise as the integrability condition of a system of linear equations and possess a binary Darboux transformation to generate exact solutions. We recover chiral models and potential forms of the self-dual Yang-Mills, as well as corresponding generalizations to higher than four dimensions, and obtain new integrable non-autonomous nonlinear matrix PDEs and corresponding systems. |
| title | Frölicher-Nijenhuis geometry and integrable matrix PDE systems |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Differential Geometry 37K10, 35Qxx, 53Z05 |
| url | https://arxiv.org/abs/2409.01328 |