Self-similar solutions and converging shocks in a non-ideal gas with dust particles

In this paper, we have used the Lie group of transformations and obtained the whole range of self-similar solutions to the problem of propagation of shock waves through a non-ideal, dusty gas. The conditions essential for the existence of similarity solutions for a strong shock are discussed. The problem of imploding (converging) shock wave is also worked out and the effects of the mass concentration of the dust particles, ratio of the density of solid particles to that of initial density of the medium, the relative specific heat and the effect of the non-ideal parameter, on the shock formation has been studied in detail.