Principle of an a priori use of symmetries in the theory of nonlinear waves

The principle of an a priori use of symmetries is proposed as a new approach to solving nonlinear problems on the basis of a reasonable complication of mathematical models. Such a complication often causes an additional symmetry and, hence, opens up possibilities for finding new analytical solutions. The application of group analysis to the problems of nonlinear acoustics is outlined. The potentialities of the proposed approach are illustrated by exact solutions, which are of interest for wave theory.