New Lie systems from Goursat distributions: reductions and reconstructions
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918183011614720 |
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| author | Carballal, Oscar |
| author_facet | Carballal, Oscar |
| contents | We show that types of bracket-generating distributions lead to new classes of Lie systems with compatible geometric structures. Specifically, the $n$-trailer system is analysed, showing that its associated distribution is related to a Lie system if $n = 0$ or $n = 1$. These systems allow symmetry reductions and the reconstruction of solutions of the original system from those of the reduced one. The reconstruction procedure is discussed and indicates potential extensions for studying broader classes of differential equations through Lie systems and new types of superposition rules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06231 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New Lie systems from Goursat distributions: reductions and reconstructions Carballal, Oscar Dynamical Systems Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems 34A26 (Primary), 34C14, 34K17, 58A30 (Secondary) We show that types of bracket-generating distributions lead to new classes of Lie systems with compatible geometric structures. Specifically, the $n$-trailer system is analysed, showing that its associated distribution is related to a Lie system if $n = 0$ or $n = 1$. These systems allow symmetry reductions and the reconstruction of solutions of the original system from those of the reduced one. The reconstruction procedure is discussed and indicates potential extensions for studying broader classes of differential equations through Lie systems and new types of superposition rules. |
| title | New Lie systems from Goursat distributions: reductions and reconstructions |
| topic | Dynamical Systems Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems 34A26 (Primary), 34C14, 34K17, 58A30 (Secondary) |
| url | https://arxiv.org/abs/2505.06231 |