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29 March 2024
 
  » arxiv » nlin.SI/0405069

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Group classification of nonlinear wave equations
V.I.Lagno ; R.Z. Zhdanov ; O.Magda ;
Date 31 May 2004
Subject Exactly Solvable and Integrable Systems | nlin.SI
AffiliationState Pedagogical University, Poltava), R.Z. Zhdanov (Institute of Mathematics, Kiev) and O.Magda (Institute of Mathematics, Kiev
AbstractWe 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.
Source arXiv, nlin.SI/0405069
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