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We present general analytic results for nonlinear wave phenomena in self-gravitating fluid systems, with an emphasis on applications to molecular clouds. We show that a wide class of physical systems can be described by introducing the concept of a ``charge density'' $q(\rho)$; this quantity replaces the density on the right hand side of the Poisson equation for the gravitational potential. We use this formulation to prove general results about nonlinear wave motions in self-gravitating systems. We show that in order for stationary waves to exist, the total charge (the integral of the charge density over the wave profile) must vanish. This ``no-charge'' property is closely related to the property of a system to be stable to Jeans-type perturbations for arbitrarily long wavelengths. We study nonlinear wave motions for Jeans-type theories (where $q(\rho) = \rho - \rho_0$) and find that nonlinear waves of large amplitude are confined to a rather narrow range of wavelengths. We also consider wave motions for molecular clouds threaded by magnetic fields. Finally, we discuss the implications of this work for molecular cloud structure.
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