Symmetry Transforms, Global Plasma Equilibria and Homotopy Analysis Method
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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. 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. Second chapter deals with a study of symmetry transforms for ideal MHD equations which comes from the work of Bogoyavlenskij . 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  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.