Affiliation:
1. School of Mathematics, Institute of Science Suranaree University of Technology Nakhon Ratchasima Thailand
Abstract
AbstractThe paper analyzes one of the models of equations of magnetohydrodynamics (MHD) derived earlier. The model was obtained as a result of group classification of the MHD equations in mass Lagrangian coordinates, where all dependent variables in Eulerian coordinates depend on time and two spatial coordinates. The use of Lagrangian coordinates made it possible to solve four equations, which led to the form of reduced equations containing four arbitrary functions: entropy and a three‐dimensional vector associated with the magnetic field. The objective of this work is to develop conservation laws and exact solutions for the model. Conservation laws are obtained using Noether's theorem, while exact solutions are obtained either explicitly or by solving a system of ordinary or partial differential equations with two independent variables. Numerical methods are employed for the latter solutions.
Reference21 articles.
1. OvsiannikovLV.Group Properties of Differential Equations. Izdat. Sibirsk Otdel. Akad. Nauk S.S.S.R.; 1962 G Bluman English trans. 1967.
2. OvsiannikovLV.Group Analysis of Differential Equations. Nauka; 1978 English trans. WFAmes ed. published byAcademic Press;1982.
3. IbragimovNH.Transformation Groups Applied to Mathematical Physics. Nauka; 1983 English transl. DReidel ed. Dordrecht 1985.
4. Applications of Lie Groups to Differential Equations
5. Invariante Variationsprobleme, Nachr. d. Königlichen Gesellschaft der Wissenschaften zu Göttingen;Noether E;Mathematisch‐Physikalische Klasse Heft,1918