The propagation of dust-acoustic waves in a dusty plasma bounded in finite symmetrical cylindrical geometry has been theoretically investigated. By using the reductive perturbation method, we obtain a quasi-nonlinear Schrödinger equation. It is shown that there is a dark envelope soliton under certain conditions, while its amplitude will decrease with the time. The dependence of both the dispersion relation and group velocity of envelope solitary waves on the radius of cylinder has been given. Moreover, we define the duration time of dark envelope solitons and give the theoretical ones. It is found that the duration time increases as the radius of cylinder increases, while it decreases as the viscosity coefficient of dusty plasmas increases.

从理论上研究了尘埃声波在有限对称圆柱几何形状中的尘埃等离子体中的传播。通过使用归纳摄动法，我们得到了一个准非线性薛定ding方程。结果表明，在一定条件下存在一个暗包络孤子，其振幅会随着时间而减小。给出了包络孤波的色散关系和群速度对圆柱半径的依赖关系。此外，我们定义了暗包孤孤子的持续时间，并给出了理论上的时间。发现持续时间随着圆柱半径的增加而增加，而随着粉尘等离子体的粘度系数的增加而减小。