Group classification of nonlinear wave equations

Lagno, V. I.; Zhdanov, R. Z.; Magda, O.

Group classification of nonlinear wave equations

Authors

Lagno, V. I.

Zhdanov, R. Z.

Magda, O.

Description

We perform complete group classification of the general class of quasi linear wave equations in two variables. This class may be seen as a broad generalization of the nonlinear d'Alembert, Liouville, sin/sinh-Gordon and Tzitzeica equations. In this way we derived a number of new genuinely nonlinear invariant models with high symmetry properties. In particular, we obtain four classes of nonlinear wave equations admitting five-dimensional invariance groups. Applying the symmetry reduction technique we construct multi-parameter families of exact solutions of those wave equations.
56 pages, LaTeX