Asymptotic Methods for Nonlinear Magnetospheric Boundary Waves

This work presents theoretical results concerning nonlinear wave propagation along boundaries between conducting fluids permeated by a magnetic field, using magnetohydrodynamics (MHD) as the basic means of description. The propagation of surface waves at interfaces between two media is a fundamental physical process, which is as important for the dynamics of structured systems of various nature as the ordinary bulk waves are for homogeneous media. The surface waves are, by definition, spatially localized disturbances propagating along an interface, which itself deforms in a way consistent with the mode structure. As a fundamental phenomenon behind the motion of boundaries, the surface modes are important in many situations that arise in geophysics, space physics, astrophysics and other areas. The motivation for this study comes from the area of magnetospheric physics. The boundary of the Earth's magnetosphere--the magnetopause--is an important example of a naturally existing interface, which can be sometimes adequately described as a tangential discontinuity (TD) between the solar wind and the magnetospheric plasmas and magnetic fields. For stable and Kelvin-Helmholtz unstable surface waves on MHD tangential discontinuity, reduced nonlinear governing equations are derived, using appropriate techniques for nonlinear evanescent waves. The evolution of waves, as described by the reduced equations, is studied by analytical and numerical methods.