由於觀測到的鄰近螺旋星系的旋轉曲線在靠近中心處（<1 kpc）都近似剛體轉動，而密度波理論主要是解釋在較差自轉系統下的星系螺旋狀構造，所以我們想探討在剛體轉動的情形下，也就是在星系靠近中央的地方，密度波理論是否也成立。我們發現密度波在剛體轉動下依然存在，在線性理論中，波是由白塞耳方程式（Bessel equation）所主導的，而旋臂的螺傾角愈接近中央愈大，直至垂直插入中心。這些波跟星系中央的氣體塵埃盤上的螺旋和棒狀結構極有關聯。我們將提出在沒有棒狀位勢下，接近星系中央的密度波的線性及非線性理論。當沒有棒狀構造出現在星系中心時，這些波可能是由聲波－曲率不穩定性所引起的（Montenegro, Yuan, & Elmergreen 1998）。我們將我們得到的結果與哈伯太空望遠鏡所觀測到的NGC 2207的影像及用小波處理過後的影像做比較。 The observed rotation laws near the center $(<1 kpc)$ for almost all 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.
