中文摘要：

从理论上研究了非热离子、外部磁场、碰撞对非均匀热尘埃等离子体中三维非线性尘埃声孤波的影响。运用约化摄动法得到描述三维非线性尘埃声孤波的非标准的变系数Korteweg-deVries（KdV）方程。然后把非标准KdV方程变为标准的变系数KdV方程，并且得到了标准的变系数KdV方程的近似解析解。由此解析解可以看出，非热离子的数目、碰撞、非均匀性、波的斜向传播、尘埃颗粒和非热离子的温度对三维非线性尘埃声孤波的振幅和宽度有很大的影响。外部磁场对三维非线性尘埃声孤波的宽度有影响，而对其振幅没有影响。此外，波的相速度与非热离子、波的斜向传播、尘埃颗粒的温度和非均匀性有关。

英文摘要：

The effects of the nonthermally distributed ions, the external magnetized field, and collisions on 3- D nonlinear dust acoustic solitary waves in inhomogeneous hot dusty plasmas have been investigated theoretically. A modified variable coefficients Korteweg-de Vries （MKdV） equation governing the 3-D nonlinear dust acoustic solitary waves have been derived by the reductive perturbation method. The approximate analytical so- lution of standard variable coefficients KdV equation derived from modified variable coefficients KdV equation has been obtained. This approximate analytical solution shows that nonthermal ions, inhomogeneity, collision, the oblique propagation of waves, the temperatures of dust and ions have effect on amplitude and width of 3-D nonlinear dust acoustic solitary waves. The amplitude of solitary waves is independent on the external magnetized field, but the width of solitary waves is dependent on the external magnetized field. Moreover, The phase velocity of waves is dependent on nonthermal ions, the oblique propagation of waves, the temperatures of dust and inhomogeneity.