Group classification of nonlinear wave equations

We perform complete group classification of the general class of quasi linearwave equations in two variables. This class may be seen as a broadgeneralization of the nonlinear d'Alembert, Liouville, sin/sinh-Gordon andTzitzeica equations. In this way we derived a number of new genuinely nonlinearinvariant models with high symmetry properties. In particular, we obtain fourclasses of nonlinear wave equations admitting five-dimensional invariancegroups. Applying the symmetry reduction technique we construct multi-parameterfamilies of exact solutions of those wave equations.