We have performed numerical analysis of the one‐dimensional dynamics of the cylindrical/spherical dust ion acoustic shock waves in unmagnetized dusty plasma consisting of positive ions, immobile dust particles, and nonextensive distributed cold and hot electrons. A multiple‐scale expansion method is used to derive Burgers Equation (BE) and modified Burgers equation (MBE) by including higher order nonlinearity. The basic characteristics of the shock waves have been analysed numerically and graphically for different physical parameters relevant to Saturn' E ring through 2D figures. The parametric dependence of dust ion acoustic shock waves on some plasma parameters nonextensive index, density, and temperature of cold and hot electrons, concentration of dust particles, thermal effects and kinematic viscosity of ions is explored. Furthermore, it is found that the nonplanar geometry effects have an important impact on the establishment of shock waves. The amplitude of the wave decreases faster as one departs away from the axis of the cylinder or centre of the sphere. Such decaying behaviour continues as time progresses. It is also found that an increasing dust concentration decreases the amplitude of the dust ion acoustic shock waves.

中文翻译：

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与土星E环有关的尘埃等离子体中具有两个温度电子的圆柱形和球形尘埃离子声波的参数研究

我们对由正离子，固定的尘埃颗粒以及不广泛分布的冷热电子组成的未磁化尘埃等离子体中的圆柱/球形尘埃离子声波的一维动力学进行了数值分析。通过包含更高阶的非线性，采用了多尺度展开方法来推导Burgers方程（BE）和修正的Burgers方程（MBE）。已经通过2D数字对与土星E环相关的不同物理参数进行了数值和图形分析，分析了冲击波的基本特征。探讨了粉尘离子声波对某些等离子体参数的不相关性，包括冷，热电子的非膨胀指数，密度和温度，粉尘颗粒的浓度，离子的热效应和运动粘度。此外，发现非平面几何效应对冲击波的建立有重要影响。当一个波从圆柱的轴线或球的中心离开时，波的振幅减小得更快。随着时间的流逝，这种衰减行为继续进行。还发现增加的粉尘浓度降低了粉尘离子声冲击波的幅度。