تقرير
Lagrangian multiforms on Lie groups and non-commuting flows
| العنوان: | Lagrangian multiforms on Lie groups and non-commuting flows |
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| المؤلفون: | Caudrelier, Vincent, Nijhoff, Frank, Sleigh, Duncan, Vermeeren, Mats |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Mathematical Physics Nonlinear Sciences |
| مصطلحات موضوعية: | Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematical Physics |
| الوصف: | We describe a variational framework for non-commuting flows, extending the theories of Lagrangian multiforms and pluri-Lagrangian systems, which have gained prominence in recent years as a variational description of integrable systems in the sense of multidimensional consistency. In the context of non-commuting flows, the manifold of independent variables, often called multi-time, is a Lie group whose bracket structure corresponds to the commutation relations between the vector fields generating the flows. Natural examples are provided by superintegrable systems for the case of Lagrangian 1-form structures, and integrable hierarchies on loop groups in the case of Lagrangian 2-forms. As particular examples we discuss the Kepler problem, the rational Calogero-Moser system, and a generalisation of the Ablowitz-Kaup-Newell-Segur system with non-commuting flows. We view this endeavour as a first step towards a purely variational approach to Lie group actions on manifolds. Comment: 51 pages. v2: author accepted manuscript |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.geomphys.2023.104807 |
| URL الوصول: | http://arxiv.org/abs/2204.09663 |
| رقم الأكسشن: | edsarx.2204.09663 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.geomphys.2023.104807 |
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