Group classification of nonlinear wave equations

Details Group classification of nonlinear wave equations Group classification of nonlinear wave equations

2004-05-31

arxiv.org/abs/nlin/0405069v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

56 pages, LaTeX

Scientific paper

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.

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