Multi-dimensional optimal system and conservation laws for Chaplygin gas Cargo-LeRoux model

Abstract

The well-known Cargo-LeRoux model for the isentropic Chaplygin gas is investigated using classical Lie symmetry method. Optimal systems up to six dimensions are constructed using the adjoint transformation and the invariants of the admitted Lie algebras. We develop exact solutions to the Cargo-LeRoux model by using the one-dimensional optimal system and discussed the physical behavior of such solutions graphically. Conservation laws to the governing equations are also obtained by using the nonlinear self-adjointness of the model. The performance of the developed solutions is explored through the evolutionary behavior of a discontinuity wave.