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Group Classification and Exact Solutions of Nonlinear Wave Equations

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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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Authors and Affiliations

  1. State Pedagogical University, 2 Ostrogradskogo Street, 36000, Poltava, Ukraine

    V. Lahno

  2. Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivska Street, 01601, Kyiv, Ukraine

    R. Zhdanov & O. Magda

Authors
  1. V. Lahno
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  2. R. Zhdanov
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  3. O. Magda
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Correspondence to R. Zhdanov.

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Lahno, V., Zhdanov, R. & Magda, O. Group Classification and Exact Solutions of Nonlinear Wave Equations. Acta Appl Math 91, 253–313 (2006). https://doi.org/10.1007/s10440-006-9039-0

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  • DOI: https://doi.org/10.1007/s10440-006-9039-0

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