Self-similar behavior of shock waves in generalized Chaplygin gas

This study presents a semi-analytical investigation of shock wave structures in a medium governed by the generalized Chaplygin gas equation of state, characterized by an inverse-power-law relationship between pressure and density. Employing self-similarity transformations, the governing system of nonlinear partial differential equations is reduced to an ordinary differential equation framework. The Lie group theoretic method is used to derive all possible cases of self-similar solutions. Three of the four classes of solutions that result from identifying the generators of the Lie group using invariant surface conditions admit self-similar solutions that correspond to power-law or exponential-law shock paths. To demonstrate how the reduced flow variables depend on different physical parameters, including the equation of state parameter and shock symmetry, they are calculated numerically and graphically. A closed-form particular solution of the governing model is also obtained, and its physical behavior is examined through graphical representations. The findings have important implications for both laboratory and astrophysical plasma systems and shed light on the behavior of flow variables behind the shock front.