دورية أكاديمية
Finding symmetries for the problem of water waves with surface tension
| العنوان: | Finding symmetries for the problem of water waves with surface tension |
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| المؤلفون: | E.R. Shamardina |
| المصدر: | Дифференциальная геометрия многообразий фигур, Iss 53, Pp 135-147 (2022) |
| بيانات النشر: | Immanuel Kant Baltic Federal University, 2022. |
| سنة النشر: | 2022 |
| المجموعة: | LCC:Mathematics |
| مصطلحات موضوعية: | differential equations, symmetries, hamiltonian structure, wave problem, Mathematics, QA1-939 |
| الوصف: | T. Brooke Benjamin and P. J. Olver “Hamiltonian structure, symmetries and conservation laws for water waves” study the behavior of Hamiltonian systems with an infinite-dimensional phase space. The methods of variational problems and infinite-dimensional differential geometry are applicable to this problem. A special case of the problem is an abstract problem of hydrodynamics for an ideal fluid. Its configuration space is the group of volume-preserving diffeomorphisms of some manifold in or filled with fluid. Even more special is the problem of waves on water. Its non-standard nature is due to the presence of boundary conditions on the free surface. These boundary conditions can be interpreted in terms of the functional derivatives of the energy integral, which plays the role of the Hamiltonian. Here we consider in detail the case of this problem in R2, taking into account surface tension, and find symmetries for it, which was not considered in detail in the article. Finding symmetries can be achieved without recourse to the Hamiltonian structure of the given problem. |
| نوع الوثيقة: | article |
| وصف الملف: | electronic resource |
| اللغة: | English Russian |
| تدمد: | 0321-4796 2782-3229 |
| Relation: | https://doaj.org/toc/0321-4796; https://doaj.org/toc/2782-3229 |
| DOI: | 10.5922/0321-4796-2022-53-13 |
| URL الوصول: | https://doaj.org/article/fb0dd317729742db8c0118fee6aeade3 |
| رقم الأكسشن: | edsdoj.fb0dd317729742db8c0118fee6aeade3 |
| قاعدة البيانات: | Directory of Open Access Journals |
Full Text Finder | تدمد: | 03214796 27823229 |
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| DOI: | 10.5922/0321-4796-2022-53-13 |