تقرير
Symmetries and conservation laws of the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates
| العنوان: | Symmetries and conservation laws of the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates |
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| المؤلفون: | Meleshko, S. V., Dorodnitsyn, V. A., Kaptsov, E. I. |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Mathematical Physics Physics (Other) |
| مصطلحات موضوعية: | Physics - Fluid Dynamics, Mathematical Physics, 76B07 |
| الوصف: | Symmetries of the one-dimensional shallow water magnetohydrodynamics equations (SMHD) in Gilman's approximation are studied. The SMHD equations are considered in case of a plane and uneven bottom topography in Lagrangian and Eulerian coordinates. Symmetry classification separates out all bottom topographies which yields substantially different admitted symmetries. The SMHD equations in Lagrangian coordinates were reduced to a single second order PDE. The Lagrangian formalism and Noether's theorem are used to construct conservation laws of the SMHD equations. Some new conservation laws for various bottom topographies are obtained. The results are also represented in Eulerian coordinates. Invariant and partially invariant solutions are constructed. Comment: 21 pages, 3 tables |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1088/1751-8121/aca84a |
| URL الوصول: | http://arxiv.org/abs/2208.06219 |
| رقم الأكسشن: | edsarx.2208.06219 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1088/1751-8121/aca84a |
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