Some nonlinear problems in astrophysics

Astrophysical magnetic fields, in the hydromagnetic approximation, pose a rich class of nonlinear problems. Of primary interest is the behavior and properties of the magnetic field interacting with the plasma in the presence of gravity. Substantial progress has been made recently with these problems arising in the study of interstellar clouds, stellar structures and magnetospheres, and structures on the Sun, such as prominences, sunspots and coronal magnetic fields. This paper reviews recent theoretical work, concentrating on steady state problems and emphasizing the use of analytic methods.