Using a low-frequency, low-beta model of a magnetized plasma, several
nonlinear waves are studied. All the waves share the property that the
y have a self-consistent time-averaged current in the steady state. Th
e first wave is a one-dimensional solitary wave that propagates obliqu
ely to a static magnetic field. The wave magnetic field has a kink str
ucture, which results in the production of the time-averaged current.
A two-dimensional wave that propagates parallel to the background magn
etic field is also discussed. This is a forced wave, requiring an ante
nna structure to support it in the steady state. The characteristics o
f the two-dimensional wave are dependent upon the wave speed, which in
turn is determined by the speed of the travelling wave on the externa
l antenna.