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Basarab-Horwath, Peter; Lahno, V.; Zhdanov, Renat

doi:10.1023/a:1012667617936

“…Later on, we performed complete group classification of the most general quasi-linear evolution equation [32][33][34] u t = f (t, x, u, u x )u xx + g(t, x, u, u x ).…”

Section: Group Classification Algorithmmentioning

confidence: 99%

“…, n 0 , where n 0 is the maximal dimension of the Lie algebra admitted by the equation under study. More formally, our algorithm for group classification of the class of PDEs (1.1) consists of the following steps (for more details, see [34]):…”

Section: Group Classification Algorithmmentioning

confidence: 99%

Group Classification and Exact Solutions of Nonlinear Wave Equations

Lahno

¹

,

Zhdanov

²

,

Magda

³

2006

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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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“…Our approach to group classification of the class of PDEs (1.1) consists of the following steps (for more details, see [36]):…”

Section: Group Classification Algorithmmentioning

confidence: 99%

Group classification of nonlinear wave equations

Lahno

¹

,

Zhdanov

²

2005

Journal of Mathematical Physics

Self Cite

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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.

show abstract

“…was considered in [26]. As a result, the equivalence class was extended to equations invariant under five-dimensional Lie algebras.…”

Section: U)mentioning

confidence: 99%