Symmetry Transforms, Global Plasma Equilibria and Homotopy Analysis Method.

摘要

Magnetohydrodynamics (MHD) flows and equations have been the focus of a large number of researchers. Here a study of such flows and equations is presented.;Second chapter deals with a study of symmetry transforms for ideal MHD equations which comes from the work of Bogoyavlenskij [18]. Different properties of such transforms are also discussed which include the infinite-dimensional Abelian group formed by the symmetries, breaking of geometrical symmetries and ball lightning phenomenon.;Next we review the recent work of Bogoyavlenskij [19] to present the derivation of exact plasma equilibria with axial and helical symmetries. Asymptotic and periodic nature of the obtained solutions has also been studied.;The last chapter comprises of my own results and it deals with finding solution to unsteady thin film flow of a magnetohydrodynamic fluid. Governing equations of such flows are often very complex and nonlinear. So, we use Homotopy Analysis Method to find exact solution to such nonlinear equations.;The first chapter contains a brief introduction to Homotopy Analysis Method (HAM) along with some other definitions. A detailed example on the application of HAM is also included to further clarify the scheme of the method.