nearby spiral galaxies can be approximated by a rigid-body rotation.
The density-wave theory of galactic spirals is tailored to handling a
differentially rotating system.
Whether it can survive in a system of rigid-body rotation and, if it can,
how it works in that system deserves a simple answer.
We find indeed it does. Actually, in the linear theory, the waves are
governed by the Bessel equations if the ambient density is constant.
The pitch angle of the spirals increases to reach $90^{circ}$ while the
spirals approaching to the center. These waves are very relevant to the study
of the spiral-bar structures in the gas-dust disk found in the galactic
central regions. We present a linear and a non-linear theory of the spiral
density waves near the center without a driving bar potential.
When it is without the presence of the bar, we believe the waves are caused
by an acoustic-curvature instability (Montenegro, Yuan & Elmergreen 1998).
We compare our results with the HST observations of NGC 2207 and its image
obtained by using the wavelet method.

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