Group classification of nonlinear wave equations

We perform complete group classification of the general class of quasilinear wave equations in two variables. This class may be seen as a generalization of the nonlinear d’Alembert, Liouville, sin∕sinh-Gordon and Tzitzeica equations. We derive a number of new genuinely nonlinear invariant models with high symmetry properties. In particular, we obtain four classes of nonlinear wave equations that admit five-dimensional invariance groups.