General Analytic Results for Nonlinear Waves and Solitons in Molecular Clouds
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**Session 68 -- Star Formation**
*Oral presentation, Thursday, 10:30-12:00, Zellerbach Playhouse Room*

## [68.03] General Analytic Results for Nonlinear Waves and Solitons in Molecular Clouds

*F. C. Adams, M. Fatuzzo, and R. Watkins (U. Michigan)*
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.

**Thursday
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