Large-amplitude magnetohydrodynamic waves in nonhomogeneous plasmas

We consider the propagation of large-amplitude magnetohydrodynamic (MHD) waves in an anisotropic nonhomogeneous plasma. A classical MHD formulation is adopted, and, by means of a sequence of transformations and use of Elsasser's variables, we derive an exact nonlinear system of equations in compact form that describes such waves. The system incorporates compressibility of the plasma and an arbitrary polarization for the waves. Accordingly, the system provides for the analysis of parallel-propagating, nonlinear Alfven waves and magnetosonic waves in a general space plasma context, including the solar wind. We obtain a new large-amplitude incompressible Alfven wave solution to the system, and also show how to construct Riemann solutions that are valid under broad assumptions. Brief consideration is given to Alfven wave propagation in a stationary plasma, and we show that the equation of propagation reduces to classical second-order partial differential equations in two special cases. For the special case in which the Alfven speed depends linearly on the spatial coordinate, a simple, exact Riemann solution is presented.