Group Classification and Exact Solutions of Nonlinear Wave Equations |
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Authors: | V. Lahno R. Zhdanov O. Magda |
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Affiliation: | (1) State Pedagogical University, 2 Ostrogradskogo Street, 36000 Poltava, Ukraine;(2) Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivska Street, 01601 Kyiv, Ukraine |
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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 these equations. |
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