Lie symmetry analysis for the Cargo-Leroux model with isentropic perturbation pressure equation of state

In this article, the well-known Cargo-Leroux model with isentropic perturbation equation of state is analyzed using the Lie symmetry method. By using invariant conditions of system of partial differential equations, six dimensional Lie algebra is obtained. The optimal system for system of partial differential equations is constructed using adjoint representation and the invariants of associated Lie algebras of the system. Further, with the help of one-dimensional optimal system invariant solutions are constructed. Also, physically significant solutions such as traveling wave solutions, specifically the kink-type solitons and peakon-type solitons are obtained by using traveling wave transformations and all the solutions are graphically demonstrated. Finally, the hyperbolic nature of system of partial differential equations is examined by studying the evolutionary behavior of a discontinuity wave.