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The formation of nonlinear structures in a self-gravitating dusty
plasma is considered when the dust dynamics includes the
electrostatic and gravitational forces on an equal footing. Here,
we obtain a Helmholtz wave equation, which describes the
propagation of stationary gravitational-electrostatic waves. The
characteristic lengths of the space regularities, as found here,
are much smaller than the wavelengths of the
gravitational-electrostatic waves. Furthermore, it is shown that
consideration of a uniform dusty plasma rotation around a fixed
axis, gives rise to a circular rotating filament structure.
Finally, the problem of the Jeans instability for circular waves
in a rotating dusty plasma is generalized, and it is found that
the purely growing Jeans instability assumes the form of a
periodic instability.
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