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Group classification of nonlinear wave equations

V. I. Lagno·R. Z. Zhdanov·O. Magda
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Abstract

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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V. I. Lagno, R. Z. Zhdanov, O. Magda. 2004-05-31. Group classification of nonlinear wave equations. https://arxiv.org/abs/nlin/0405069

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