Characteristic function method for classification of equations of hydrodynamics of a perfect fluid

The characteristic function method has been employed to determine and investigate certain classes of solution of a system of first-order nonlinear hydrodynamical equations of a perfect fluid with respect to different Coriolis parameters. The application of a one-parameter group of infinitesimal transformations reduces the number of independent variables by one, and consequently, the system of partial differential equations in two independent variables reduces to a system of ordinary differential equations. The resulting differential equations are solved analytically for some special cases.