Group Classification of Invariant Solutions of Nonlinear Wave Equations

Abstract

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