Construction of exact solutions to nonlinear equations of the hyperbolic type

TitleConstruction of exact solutions to nonlinear equations of the hyperbolic type
Publication TypeJournal Article
Year of Publication2017
AuthorsBarannyk, AF, Barannyk, TA, Yuryk, II
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
Date Published7/2017
Substitutions that reduce the equation $u_{tt} = a(t)uu_{xx} + b(t)u_{x}^{2} + c(t)u$ to a system of ordinary differential equations are considered. An efficient method to integrate the corresponding reduced systems is proposed. It is shown that their integration can be reduced to the integration of a system of linear equations $w_{1}^{''} = \Phi_{1}(t)w_{1}$, $w_{2}^{''} = \Phi_{2}(t)w_{2}$, where $\Phi_{1}(t)$ and $\Phi_{2}(t)$ are arbitrary predefined functions.
Keywordsdifferential equations, generalized separation of variables, nonlinear hyperbolic equations
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