  We study the linear evolution of small perturbations in self-gravitating
fluid systems with magnetic fields. We consider wave-like perturbations to
nonuniform filamentary and sheet-like hydrostatic equilibria in the presence of
a uniform parallel magnetic field. Motivated by observations of molecular
clouds that suggest substantial nonthermal (turbulent) pressure, we adopt
equations of state that are softer than isothermal. We numerically determine
the dispersion relation and the form of the perturbations in the regime of
instability. The form of the dispersion relation is the same for all equations
of state considered, for all magnetic field strengths, and for both geometries
examined. We demonstrate the existence of a fastest growing mode for the system
and study how its characteristics depend on the amount of turbulence and the
strength of the magnetic field. Generally, turbulence tends to increase the
rate and the length scale of fragmentation. While tending to slow the
fragmentation, the magnetic field has little effect on the fragmentation length
scale until reaching some threshold, above which the length scale decreases
significantly. Finally, we discuss the implications of these results for star
formation in molecular clouds.
