LAUSR

In this paper, we employ Lie classical symmetries to analyze the two‐dimensional isentropic Euler equations system for Chaplygin gas. Adjoint operators play an essential part in deriving an optimal system of subalgebras. Introducing a novel approach, we present a method for constructing a two‐dimensional optimal system through strategic adjoint actions which is using the largest chain of removal operators. By employing the vector fields obtained from the optimal system, we efficiently transform the governing model into a collection of ordinary differential equations. Consequently, we attain group invariant solutions and elucidate their graphical behavior. Moreover, we obtain conservation laws for the governing model by utilizing it is nonlinear self‐adjoint properties and employing the direct multiplier method.