This paper concerns with the similarity solutions using Lie group theoretic method for one-dimensional unsteady isothermal flow behind the shock wave in the mixture of non-ideal gas and small solid particles in rotating medium. Group theoretic technique brings the different possible cases of potential solutions with the power law, particular case of power law and exponential law shock paths with the different choices of constants present in the generators of the Lie group of transformations. Similarity solutions for non-ideal dusty gas (a mixture of non-ideal gas and small solid dust particles) exist if the density of the ambient medium is constant. Solutions are obtained for both exponential law and power law shock paths. The effects of the variation of the physical parameters on the flow variables distribution behind the shock wave front, and on the shock are discussed. The shock strength increases with an increase in the ratio of the specific heat of the solid particles to the specific heat of the gas at constant volume ${\beta }^{\prime }$, the initial azimuthal velocity variation index ${𝜃}_1$, and the ratio of the density of solid particles to the initial density of the gas $G_0$. The shock wave decays with an increase in the value of gas non-idealness parameter $\overline{b}$.

研究了旋转介质中非理想气体与固体小颗粒混合物中激波后一维非定常等温流动的李群理论相似解。群论技术带来了幂律的潜在解的不同可能情况，幂律的特殊情况和指数律冲击路径以及李变换的生成元中存在的常数的不同选择。如果环境介质的密度恒定，则存在非理想含尘气体（非理想气体和小的固体尘粒的混合物）的相似解。获得了指数定律和幂定律冲击路径的解。物理参数的变化对冲击波前后流动变量分布的影响，并就冲击进行了讨论。冲击强度随着固体颗粒的比热与定容气体比热之比的增加而增加${\beta }^{\text{'}}$, 初始方位速度变化指数${𝜃}_1$，以及固体粒子的密度与气体的初始密度之比$G_0$. 激波随气体非理想参数值的增加而衰减$\overline{b}$.