Exact solutions for nonlinear wave equations

A method for solving a quasilinear nonelliptical equation of the second order is developed and we give classification and parametrization of simple elements of the equation. The equation for potential stationary flow of a compressible gas in a supersonic region is considered as the first example of an application of the method . A new exact solution is obtained which may be treated as a nonlinear analogue of a stationary wave. A gauge structure for the equation and an analogue of the Baeklund transformation are introduced. Certain classes of exact solutions for an equation of a nonstationary potential flow of a compressible gas are found. This is the second example of an application of the method. Finally a physical analysis of the results is carried out.