Symmetries and conservation laws of the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates

Autor:	Meleshko, S. V., Dorodnitsyn, V. A., Kaptsov, E. I.
Rok vydání:	2022
Předmět:	Physics - Fluid Dynamics Mathematical Physics 76B07
Druh dokumentu:	Working Paper
DOI:	10.1088/1751-8121/aca84a
Popis:	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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.06219 Zobrazit plný text záznamu View this record from Arxiv