Abstract
Exact one-dimensional solutions of the magnetohydrodynamic equations of an incompressible fluid are considered. It is shown that one class of plane wave solutions of the linearized equations is also a possible class of solutions of the general equations including the effect of displacement current. A similar result is also established for the solutions for a horizontally stratified fluid. For the particular case when the viscosity is equal to the magnetic diffusivity an exact solution is obtained for the magnetohydrodynamic Rayleigh problem for a semi-infinite plate. It is shown that this solution may be employed directly to give the solution for liquids of small, but not necessarily equal, viscosity and magnetic diffusivity.
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