流体模自引力系统的调制不稳定性

Modulation Instability of Self-gravitating Systems in Stable Modes

利用流体模自引力系统的结构方程,分析了流体模自引力系统的有限振幅的调制不稳定性,解析上获得了在两种特殊条件下纵扰动的时间增长率与扰动态波数之间的函数关系。最后用数值方法得到了一般情况下纵扰动的时间增长率关于扰动态波数的数值曲线,正好将两种特殊条件下的解析结果衔接起来,使其成为一条连续的曲线。从而,表明了解析结果的可靠性。

The stability of finite amplitude of the self-gravitating system in the stable modes is examined on the basis of the nonlinear governing equations.There is a modulation instability with respect to the longitudinal perturbation and the growth rates as functions of dimensionless wave number are obtained under the special conditions for which the modulation instability occurs.In the general case,the numerical curve of the growth rate with respect to dimensionless wave number is given by using the numerical simulation method.It is shown that numerical curve of the growth rate joins with the analytical solutions and the continuous curve is obtained.