The non-linear equations of motion describing the unsteady transonic flow in cartesian coordinates are considered in this dissertation. A method known as Lie group which reduce the non-linear partial differential equation to an ordinary differential equation on the basis of the underlying symmetry structure has been used. The Lie method is quite useful in reducing a complex equation to an easy-to-handle ordinary differential equation. By employing the Lie theory, the full one-parameter infinitesimal transformation group leaving the equations of motion invariance is derived along with its associated Lie algebra. Subgroups of the full group are then used to obtain a reduction by one in the number of independent variables in the system. These reductions are continued until an ordinary differential equation is reached. A series type exact solution of these reduced ordinary differential equation is obtained which leads to a series type exact solution of the unsteady transonic flow equation. The Lie group method seems to be an appropriate choice to handle these nonlinear equation.
