  In this paper, a general equation for the evolution of an axisymmetric
magnetic field in a Hall plasma is derived, with an integral similar to the
Grad-Shafranov equation. Special solutions arising from curvature -- whistler
drift modes that propagate along the electron drift as a Burger's shock, and
nonlinear periodic and soliton-like solutions to the generalized Grad-Shafranov
integral -- are analyzed. We derive analytical and numerical solutions in a
classical electron-ion Hall plasma, in which electrons and ions are the only
species in the plasmas. Results may then be applied to the following
low-ionized astrophysical plasmas: in protostellar disks, in which the ions may
be coupled to the motion of gases; and in molecular clouds and protostellar
jets, in which the much heavier charged dust in a dusty Hall plasma may be
collisionally coupled to the gas.
